@article{MTMT:34607533,
	title = {Some New Characterizations of a Hermitian Matrix and Their Applications},
	url = {https://m2.mtmt.hu/api/publication/34607533},
	author = {Tian, Yongge},
	doi = {10.1007/s11785-023-01440-x},
	journal-iso = {COMPLEX ANAL OPER TH},
	journal = {COMPLEX ANALYSIS AND OPERATOR THEORY},
	volume = {18},
	unique-id = {34607533},
	issn = {1661-8254},
	abstract = {A square matrix A over the field of complex numbers is said to be Hermitian if A = A*, the conjugate transpose of A, while Hermitian matrices are known to be an important class of matrices. In addition to the definition, a Hermitian matrix can be characterized by some other matrix equalities. This fact can be described in the implication form f (A, A*) = 0 double left right arrow A = A*, where f (center dot) denotes certain ordinary algebraic operation of A and A*. In this note, we show two special cases of the equivalent facts: AA* A = A* AA* double left right arrow A(3) = AA* A double left right arrow A = A* without assuming the invertibility of A through the skillful use of decompositions and determinants of matrices. Several consequences and extensions are presented to a selection of matrix equalities composed of multiple products of A and A*.},
	keywords = {DETERMINANT; Matrix decomposition; Hermitian matrix; Generalized inverse; Matrix equality},
	year = {2024},
	eissn = {1661-8262}
}

@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:32083667,
	title = {On Self-Adjoint Linear Relations},
	url = {https://m2.mtmt.hu/api/publication/32083667},
	author = {Berkics, Péter},
	doi = {10.1556/314.2020.00001},
	journal-iso = {MATH PANNONICA},
	journal = {MATHEMATICA PANNONICA},
	volume = {27_NS1},
	unique-id = {32083667},
	issn = {0865-2090},
	year = {2021},
	pages = {1-7}
}

@article{MTMT:32381366,
	title = {Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory},
	url = {https://m2.mtmt.hu/api/publication/32381366},
	author = {Ita, Eyo Eyo III and Soo, Chopin and Yu, Hoi Lai},
	doi = {10.1088/1361-6382/abcb0e},
	journal-iso = {CLASSICAL QUANT GRAV},
	journal = {CLASSICAL AND QUANTUM GRAVITY},
	volume = {38},
	unique-id = {32381366},
	issn = {0264-9381},
	abstract = {The Hamiltonian of intrinsic time gravity is elucidated. The theory describes Schrodinger evolution of our universe with respect to the fractional change of the total spatial volume. Gravitational interactions are introduced by extending Klauder's momentric variable with similarity transformations, and explicit spatial diffeomorphism invariance is enforced via similarity transformation with exponentials of spatial integrals. In analogy with Yang-Mills theory, a Cotton-York term is obtained from the Chern-Simons functional of the affine connection. The essential difference is the fundamental variable for geometrodynamics is the metric rather than a gauge connection; in the case of Yang-Mills, there is also no analog of the integral of the spatial Ricci scalar curvature. Heat kernel regularization is employed to isolate the divergences of coincidence limits; apart from an additional Cotton-York term, a prescription in which Einstein's Ricci scalar potential emerges naturally from the positive-definite self-adjoint Hamiltonian of the theory is demonstrated.},
	keywords = {Einstein's theory; Intrinsic time; heat kernel regularization; Cotton-York tensor},
	year = {2021},
	eissn = {1361-6382}
}

@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:31840162,
	title = {Canonical Graph Contractions of Linear Relations on Hilbert Spaces},
	url = {https://m2.mtmt.hu/api/publication/31840162},
	author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
	doi = {10.1007/s11785-020-01066-3},
	journal-iso = {COMPLEX ANAL OPER TH},
	journal = {COMPLEX ANALYSIS AND OPERATOR THEORY},
	volume = {15},
	unique-id = {31840162},
	issn = {1661-8254},
	year = {2021},
	eissn = {1661-8262},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:31488892,
	title = {Operational calculus for rows, columns, and blocks of linear relations},
	url = {https://m2.mtmt.hu/api/publication/31488892},
	author = {Hassi, Seppo and Labrousse, Jean-Philippe and de Snoo, Henk},
	doi = {10.1007/s43036-020-00085-3},
	journal-iso = {ADV OPERAT THEORY},
	journal = {ADVANCES IN OPERATOR THEORY},
	volume = {5},
	unique-id = {31488892},
	abstract = {Columns and rows are operations for pairs of linear relations in Hilbert spaces, modelled on the corresponding notions of the componentwise sum and the usual sum of such pairs. The introduction of matrices whose entries are linear relations between underlying component spaces takes place via the row and column operations. The main purpose here is to offer an attempt to formalize the operational calculus for block matrices, whose entries are all linear relations. Each block relation generates a unique linear relation between the Cartesian products of initial and final Hilbert spaces that admits particular properties which will be characterized. Special attention is paid to the formal matrix multiplication of two blocks of linear relations and the connection to the usual product of the unique linear relations generated by them. In the present general setting these two products need not be connected to each other without some additional conditions.},
	keywords = {PRODUCT; adjoint; Linear relation; Operator matrix; Row operator; Column operator},
	year = {2020},
	eissn = {2538-225X},
	pages = {1193-1228}
}

@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}
}

@article{MTMT:31300976,
	title = {Range-kernel characterizations of operators which are adjoint of each other},
	url = {https://m2.mtmt.hu/api/publication/31300976},
	author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
	doi = {10.1007/s43036-020-00068-4},
	journal-iso = {ADV OPERAT THEORY},
	journal = {ADVANCES IN OPERATOR THEORY},
	volume = {5},
	unique-id = {31300976},
	year = {2020},
	eissn = {2538-225X},
	pages = {1026-1038},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@misc{MTMT:32083675,
	title = {Two Removal and Cancellation Laws Associated with a Complex Matrix and Its Conjugate Transpose},
	url = {https://m2.mtmt.hu/api/publication/32083675},
	author = {Yongge, Tian},
	unique-id = {32083675},
	year = {2020}
}

@article{MTMT:30440476,
	title = {Maximal Operators with Respect to the Numerical Range},
	url = {https://m2.mtmt.hu/api/publication/30440476},
	author = {Corso, Rosario},
	doi = {10.1007/s11785-018-0805-6},
	journal-iso = {COMPLEX ANAL OPER TH},
	journal = {COMPLEX ANALYSIS AND OPERATOR THEORY},
	volume = {13},
	unique-id = {30440476},
	issn = {1661-8254},
	abstract = {Let $$\\mathfrak {n}$$nbe a nonempty, proper, convex subset of $$\\mathbb {C}$$C. The $$\\mathfrak {n}$$n-maximal operators are defined as the operators having numerical ranges in $$\\mathfrak {n}$$nand are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $$\\mathfrak {n}$$n-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.},
	year = {2019},
	eissn = {1661-8262},
	pages = {781-800}
}

@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}
}

@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:3293570,
	title = {On the square root of a positive selfadjoint operator},
	url = {https://m2.mtmt.hu/api/publication/3293570},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1007/s10998-017-0192-1},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	volume = {75},
	unique-id = {3293570},
	issn = {0031-5303},
	abstract = {We provide a short, elementary proof of the existence and uniqueness of the square root in the context of unbounded positive selfadjoint operators on real or complex Hilbert spaces.},
	keywords = {SQUARE ROOT; Positive operator; selfadjoint operator; Unbounded operator},
	year = {2017},
	eissn = {1588-2829},
	pages = {268-272},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:26333739,
	title = {Selfadjoint operators and symmetric operators},
	url = {https://m2.mtmt.hu/api/publication/26333739},
	author = {Hirasawa, G},
	doi = {10.14232/actasm-015-044-4},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {82},
	unique-id = {26333739},
	issn = {0001-6969},
	year = {2016},
	pages = {529-543}
}

@article{MTMT:3084669,
	title = {Adjoint of sums and products of operators in Hilbert spaces},
	url = {https://m2.mtmt.hu/api/publication/3084669},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.14232/actasm-015-809-3},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {82},
	unique-id = {3084669},
	issn = {0001-6969},
	year = {2016},
	pages = {175-191},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:3079729,
	title = {On the sum between a closable operator T and a T-bounded operator},
	url = {https://m2.mtmt.hu/api/publication/3079729},
	author = {Popovici, D and 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 = {3079729},
	issn = {0524-9007},
	year = {2015},
	pages = {95-104},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@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}
}

@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},
	pages = {659-664},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}