@article{MTMT:34936819,
	title = {A Generalized Von Neumann's Theorem for Linear Relations in Hilbert Spaces},
	url = {https://m2.mtmt.hu/api/publication/34936819},
	author = {Roman, Marcel and Sandovici, Adrian},
	doi = {10.1007/s00025-024-02145-z},
	journal-iso = {RES MATHEM},
	journal = {RESULTS IN MATHEMATICS},
	volume = {79},
	unique-id = {34936819},
	issn = {1422-6383},
	keywords = {Hilbert space; Nonnegative linear relation; Selfadjoint linear relation; closed linear relation; Von Neumann theorem},
	year = {2024},
	eissn = {1420-9012}
}

@article{MTMT:33766588,
	title = {Extensions of positive symmetric operators and Krein's uniqueness criteria},
	url = {https://m2.mtmt.hu/api/publication/33766588},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1080/03081087.2023.2196610},
	journal-iso = {LINEAR MULTILINEAR A},
	journal = {LINEAR AND MULTILINEAR ALGEBRA},
	volume = {72},
	unique-id = {33766588},
	issn = {0308-1087},
	year = {2024},
	eissn = {1563-5139},
	pages = {1663-1688},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:34751048,
	title = {Reduction of positive self-adjoint extensions},
	url = {https://m2.mtmt.hu/api/publication/34751048},
	author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
	doi = {10.7494/OpMath.2024.44.3.425},
	journal-iso = {OPUSC MATHEMATICA},
	journal = {OPUSCULA MATHEMATICA},
	volume = {44},
	unique-id = {34751048},
	issn = {1232-9274},
	year = {2024},
	eissn = {2300-6919},
	pages = {425-438},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:34272303,
	title = {Unbounded operators having self-adjoint, subnormal, or hyponormal powers},
	url = {https://m2.mtmt.hu/api/publication/34272303},
	author = {Dehimi, Souheyb and Mortad, Mohammed Hichem},
	doi = {10.1002/mana.202100390},
	journal-iso = {MATH NACHR},
	journal = {MATHEMATISCHE NACHRICHTEN},
	volume = {296},
	unique-id = {34272303},
	issn = {0025-584X},
	abstract = {We show that if a densely defined closable operator A is such that the resolvent set of A(2) is nonempty, then A is necessarily closed. This result is then extended to the case of a polynomial p(A)$p(A)$. We also generalize a recent result by Sebestyen-Tarcsay concerning the converse of a result by J. von Neumann. Other interesting consequences are also given. One of them is a proof that if T is a quasinormal (unbounded) operator such that Tn$T<^>n$ is normal for some n & GE;2$n\ge 2$, then T is normal. Hence a closed subnormal operator T such that Tn$T<^>n$ is normal is itself normal. We also show that if a hyponormal (nonnecessarily bounded) operator A is such that Ap$A<^>p$ and Aq$A<^>q$ are self-adjoint for some coprime numbers p and q, then A must be self-adjoint.},
	keywords = {Square roots; Self-adjoint operators; Powers of operators; unbounded operators; quasinormal operators; closed operators; Hyponormal operators; Normal operators; Bezout's theorem in arithmetic; paranormal operators; relatively prime numbers; spectrum and resolvent set; subnormal operators},
	year = {2023},
	eissn = {1522-2616},
	pages = {3915-3928},
	orcid-numbers = {Dehimi, Souheyb/0000-0002-1485-4686}
}

@article{MTMT:33735457,
	title = {Certain properties involving the unbounded operators p(T), TT⁎, and T⁎T; and some applications to powers and nth roots of unbounded operators},
	url = {https://m2.mtmt.hu/api/publication/33735457},
	author = {Mortad, M.H.},
	doi = {10.1016/j.jmaa.2023.127159},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {525},
	unique-id = {33735457},
	issn = {0022-247X},
	abstract = {In this paper, we are concerned with conditions under which [p(T)]⁎=p‾(T⁎), where p(z) is a one-variable complex polynomial, and T is an unbounded, densely defined, and linear operator. Then, we deal with the validity of the identities σ(AB)=σ(BA), where A and B are two unbounded operators. The equations (TT⁎)⁎=TT⁎ and (T⁎T)⁎=T⁎T, where T is a densely defined closable operator, are also studied. A particular interest will be paid to the equation T⁎T=p(T) and its variants. Then, we have certain results concerning nth roots of classes of normal and nonnormal (unbounded) operators. Some further consequences and counterexamples accompany our results. © 2023 Elsevier Inc.},
	keywords = {self-adjoint operator; closed operator; Normal operator; Quasinormal operator; Operator polynomials; Square roots of operators},
	year = {2023},
	eissn = {1096-0813}
}

@article{MTMT:33218740,
	title = {A matrix formula for Schur complements of nonnegative selfadjoint linear relations},
	url = {https://m2.mtmt.hu/api/publication/33218740},
	author = {Contino, Maximiliano and Maestripieri, Alejandra and Marcantognini, Stefania},
	doi = {10.1016/j.laa.2022.09.003},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {654},
	unique-id = {33218740},
	issn = {0024-3795},
	abstract = {If a nonnegative selfadjoint linear relation A in a Hilbert space and a closed subspace S are assumed to satisfy that the domain of A is invariant under the orthogonal projector onto S, then A admits a particular matrix representation with respect to the decomposition S circle plus S-&updatedExpOTTOM;. This matrix representation of A is used to give explicit formulae for the Schur complement of A on S as well as the S-compression of A. (c) 2022 Elsevier Inc. All rights reserved.},
	keywords = {Linear relations; Schur complement; Shorted operators; Unbounded selfadjoint operators},
	year = {2022},
	eissn = {1873-1856},
	pages = {143-176},
	orcid-numbers = {Contino, Maximiliano/0000-0002-4158-0828}
}

@article{MTMT:32083562,
	title = {Adjoint to each other linear relations. Nieminen type criteria},
	url = {https://m2.mtmt.hu/api/publication/32083562},
	author = {Roman, Marcel and Sandovici, Adrian},
	doi = {10.1007/s00605-021-01579-9},
	journal-iso = {MONATSH MATH},
	journal = {MONATSHEFTE FUR MATHEMATIK},
	unique-id = {32083562},
	issn = {0026-9255},
	year = {2021},
	eissn = {1436-5081}
}

@article{MTMT:32083559,
	title = {Essentially self-adjoint linear relations in Hilbert spaces},
	url = {https://m2.mtmt.hu/api/publication/32083559},
	author = {Roman, Marcel and Sandovici, Adrian},
	doi = {10.1007/s10998-020-00373-8},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	volume = {83},
	unique-id = {32083559},
	issn = {0031-5303},
	year = {2021},
	eissn = {1588-2829},
	pages = {122-132}
}

@article{MTMT:31325292,
	title = {On the Adjoint of Linear Relations in Hilbert Spaces},
	url = {https://m2.mtmt.hu/api/publication/31325292},
	author = {Sandovici, Adrian},
	doi = {10.1007/s00009-020-1503-y},
	journal-iso = {MEDITERR J MATH},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {17},
	unique-id = {31325292},
	issn = {1660-5446},
	year = {2020},
	eissn = {1660-5454}
}

@misc{MTMT:32083554,
	title = {Unbounded operators having self-adjoint or normal powers and some related results},
	url = {https://m2.mtmt.hu/api/publication/32083554},
	author = {Souheyb, Dehimi and Mohammed, Hichem Mortad},
	unique-id = {32083554},
	year = {2020}
}

@article{MTMT:31096291,
	title = {On a theorem of Z. Sebestyen and Zs. Tarcsay},
	url = {https://m2.mtmt.hu/api/publication/31096291},
	author = {Gesztesy, Fritz and Schmuedgen, Konrad},
	doi = {10.14232/actasm-018-295-y},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {85},
	unique-id = {31096291},
	issn = {0001-6969},
	abstract = {We reprove a recent result of Z. Sebestyen and Zs. Tarcsay [9]: If T*T and TT* are self-adjoint, then T is closed.},
	keywords = {von Neumann's theorem},
	year = {2019},
	eissn = {2064-8316},
	pages = {291-293}
}

@article{MTMT:31093434,
	title = {Factorized sectorial relations, their maximal-sectorial extensions, and form sums},
	url = {https://m2.mtmt.hu/api/publication/31093434},
	author = {Hassi, Seppo and Sandovici, Adrian and de Snoo, Henk},
	doi = {10.1215/17358787-2019-0003},
	journal-iso = {BANACH J MATH ANAL},
	journal = {BANACH JOURNAL OF MATHEMATICAL ANALYSIS},
	volume = {13},
	unique-id = {31093434},
	issn = {2662-2033},
	abstract = {In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H. Our particular interest is in sectorial relations S, which can be expressed in the factorized formS = T* (I + iB)T or S = T (I + iB)T*;where B is a bounded self-adjoint operator in a Hilbert space K and T : H -> K (or T : K -> H, respectively) is a linear operator or a linear relation which is not assumed to be closed. Using the speci fi c factorized form of S, a description of all the maximal-sectorial extensions of S is given, along with a straightforward construction of the extreme extensions S-F, the Friedrichs extension, and S-K, the Krein extension of S, which uses the above factorized form of S. As an application of this construction, we also treat the form sum of maximal-sectorial extensions of two sectorial relations.},
	keywords = {Friedrichs extension; form sum; extremal extension; sectorial relation; Krein extension},
	year = {2019},
	eissn = {1735-8787},
	pages = {538-564}
}

@article{MTMT:30440389,
	title = {A range matrix-type criterion for the self-adjointness of symmetric linear relations},
	url = {https://m2.mtmt.hu/api/publication/30440389},
	author = {Sandovici, A.},
	doi = {10.1007/s10474-018-0883-y},
	journal-iso = {ACTA MATH HUNG},
	journal = {ACTA MATHEMATICA HUNGARICA},
	volume = {158},
	unique-id = {30440389},
	issn = {0236-5294},
	abstract = {The main objective of this paper is to provide a range-type criterion for the self-adjointness of symmetric linear relations in real or complex Hilbert spaces. The main used ingredient is a matrix whose entries are certain linear relations.},
	year = {2019},
	eissn = {1588-2632},
	pages = {27-35}
}

@article{MTMT:30440374,
	title = {Self-adjointness and skew-adjointness criteria involving powers of linear relations},
	url = {https://m2.mtmt.hu/api/publication/30440374},
	author = {Sandovici, Adrian},
	doi = {10.1016/j.jmaa.2018.09.063},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {470},
	unique-id = {30440374},
	issn = {0022-247X},
	abstract = {The main objective of this paper is to provide range-type criteria for the self-adjointness of symmetric linear relations and for the skew-adjointness of skew-symmetric linear relations in real or complex Hilbert spaces, respectively. These range-type criteria involve powers of linear relations.},
	keywords = {Hilbert space; Symmetric linear relation; Nonnegative linear relation; Selfadjoint linear relation; Skew-symmetric linear relation; Skew-adjoint linear relation},
	year = {2019},
	eissn = {1096-0813},
	pages = {186-200}
}

@article{MTMT:30446535,
	title = {On the adjoint of Hilbert space operators},
	url = {https://m2.mtmt.hu/api/publication/30446535},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1080/03081087.2018.1430120},
	journal-iso = {LINEAR MULTILINEAR A},
	journal = {LINEAR AND MULTILINEAR ALGEBRA},
	volume = {67},
	unique-id = {30446535},
	issn = {0308-1087},
	abstract = {In general, it is a non-trivial task to determine the adjoint S* of an unbounded operator S acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator T to be identical with S*. In our considerations, a central role is played by the operator matrix M-S,M-T = (I -T S I). Our approach has several consequences such as characterizations of closed, normal, skew- and selfadjoint, unitary and orthogonal projection operators in real or complex Hilbert spaces. We also give a self-contained proof of the fact that T*T always has a positive selfadjoint extension.},
	keywords = {Positive operator; selfadjoint operator; adjoint; closed operator},
	year = {2019},
	eissn = {1563-5139},
	pages = {625-645},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@misc{MTMT:31329167,
	title = {A class of sectorial relations and the associated closed forms},
	url = {https://m2.mtmt.hu/api/publication/31329167},
	author = {Seppo, Hassi and Henk, de Snoo},
	unique-id = {31329167},
	year = {2019}
}

@misc{MTMT:27207408,
	title = {Some Remarks on the Operator T^* T},
	url = {https://m2.mtmt.hu/api/publication/27207408},
	author = {Gesztesy, Fritz and Schmüdgen, Konrad},
	unique-id = {27207408},
	year = {2018}
}

@article{MTMT:27565733,
	title = {Von Neumann's theorem for linear relations},
	url = {https://m2.mtmt.hu/api/publication/27565733},
	author = {Sandovici, Adrian},
	doi = {10.1080/03081087.2017.1369930},
	journal-iso = {LINEAR MULTILINEAR A},
	journal = {LINEAR AND MULTILINEAR ALGEBRA},
	volume = {66},
	unique-id = {27565733},
	issn = {0308-1087},
	year = {2018},
	eissn = {1563-5139},
	pages = {1750-1756}
}

@article{MTMT:27080636,
	title = {Extremal maximal sectorial extensions of sectorial relations},
	url = {https://m2.mtmt.hu/api/publication/27080636},
	author = {Hassi, S and Sandovici, A and de Snoo, H S V and Winkler, H},
	doi = {10.1016/j.indag.2017.07.003},
	journal-iso = {INDAGAT MATH NEW SER},
	journal = {INDAGATIONES MATHEMATICAE-NEW SERIES},
	volume = {28},
	unique-id = {27080636},
	issn = {0019-3577},
	year = {2017},
	eissn = {1872-6100},
	pages = {1019-1055}
}

@article{MTMT:2969008,
	title = {Characterizations of essentially self-adjoint and skew-adjoint operators},
	url = {https://m2.mtmt.hu/api/publication/2969008},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1556/012.2015.52.3.1300},
	journal-iso = {STUD SCI MATH HUNG},
	journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
	volume = {52},
	unique-id = {2969008},
	issn = {0081-6906},
	abstract = {An extension of von Neumann's characterization of essentially selfadjoint operators is given among not necessarily densely defined symmetric operators which are assumed to be closable. Our arguments are of algebraic nature and follow the idea of [1]. © 2015 Akadémiai Kiadó, Budapest.},
	keywords = {Symmetric operators; Skewadjoint operators; Skew-symmetric operators; Essentially selfadjoint operators},
	year = {2015},
	eissn = {1588-2896},
	pages = {371-385},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:3079747,
	title = {Operators having selfadjoint squares},
	url = {https://m2.mtmt.hu/api/publication/3079747},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	journal-iso = {ANN UNIV SCI BP R EÖTVÖS NOM SECT MATH},
	journal = {ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EÖTVÖS NOMINATAE - SECTIO MATHEMATICA},
	volume = {58},
	unique-id = {3079747},
	issn = {0524-9007},
	year = {2015},
	pages = {105-110},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@misc{MTMT:24777434,
	title = {Factorization, majorization, and domination for linear relations},
	url = {https://m2.mtmt.hu/api/publication/24777434},
	author = {Hassi, Seppo},
	unique-id = {24777434},
	year = {2014}
}

@article{MTMT:2853826,
	title = {A reversed von Neumann theorem},
	url = {https://m2.mtmt.hu/api/publication/2853826},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.14232/actasm-013-283-x},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {80},
	unique-id = {2853826},
	issn = {0001-6969},
	year = {2014},
	eissn = {2064-8316},
	pages = {659-664},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:2542482,
	title = {Closed range positive operators on Banach spaces},
	url = {https://m2.mtmt.hu/api/publication/2542482},
	author = {Tarcsay, Zsigmond},
	doi = {10.1007/s10474-013-0380-2},
	journal-iso = {ACTA MATH HUNG},
	journal = {ACTA MATHEMATICA HUNGARICA},
	volume = {142},
	unique-id = {2542482},
	issn = {0236-5294},
	abstract = {A bounded positive operator on a Hilbert space has closed range if and only if the operator and its square root have common ranges. We give an extension of this result for positive operators acting on reflexive Banach spaces. Some other results concerning positive operators on Hilbert spaces are carried over to this general case. © 2013 Akadémiai Kiadó, Budapest, Hungary.},
	keywords = {Positive operator; THEOREMS; Kernels; reflexive Banach space; operator factorization; closed range operator; 47B65; 47A05},
	year = {2014},
	eissn = {1588-2632},
	pages = {494-501},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:2541922,
	title = {CHARACTERIZATIONS OF SELFADJOINT OPERATORS},
	url = {https://m2.mtmt.hu/api/publication/2541922},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1556/SScMath.50.2013.4.1252},
	journal-iso = {STUD SCI MATH HUNG},
	journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
	volume = {50},
	unique-id = {2541922},
	issn = {0081-6906},
	abstract = {The purpose of this paper is to revise von Neumann's characterizations of selfadjoint operators among symmetric ones. In fact, we do not assume that the underlying Hilbert space is complex, nor that the corresponding operator is densely defined, moreover, that it is closed. Following Arens, we employ algebraic arguments instead of the geometric approach of von Neumann using the Cayley transform.},
	keywords = {characterization; PERTURBATION; Positive operator; HILBERT-SPACE; selfadjoint operator; Symmetric operator},
	year = {2013},
	eissn = {1588-2896},
	pages = {423-435},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:2385712,
	title = {On form sums of positive operators},
	url = {https://m2.mtmt.hu/api/publication/2385712},
	author = {Tarcsay, Zsigmond},
	doi = {10.1007/s10474-013-0299-7},
	journal-iso = {ACTA MATH HUNG},
	journal = {ACTA MATHEMATICA HUNGARICA},
	volume = {140},
	unique-id = {2385712},
	issn = {0236-5294},
	abstract = {The purpose of the present note is to provide domain, kernel and range characterizations for the form sum of two positive selfadjoint operators. In addition, we establish a criterion for the closedness of the range of the form sum and give the Moore-Penrose pseudoinverse in this case. © 2013 Akadémiai Kiadó, Budapest, Hungary.},
	keywords = {Positive operator; Krein-von Neumann extension; closed range; range characterization; Moore-Penrose pseudoinverse; form sum; domain characterization; 47B25; 47A20},
	year = {2013},
	eissn = {1588-2632},
	pages = {187-201},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}