@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}
}

@misc{MTMT:32085481,
	title = {Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory},
	url = {https://m2.mtmt.hu/api/publication/32085481},
	author = {Eyo, Eyo Ita III and Chopin, Soo and Hoi-Lai, Yu},
	unique-id = {32085481},
	year = {2021}
}

@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: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: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: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: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}
}

@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}
}