TY - JOUR AU - Tian, Yongge TI - Some New Characterizations of a Hermitian Matrix and Their Applications JF - COMPLEX ANALYSIS AND OPERATOR THEORY J2 - COMPLEX ANAL OPER TH VL - 18 PY - 2024 IS - 1 PG - 8 SN - 1661-8254 DO - 10.1007/s11785-023-01440-x UR - https://m2.mtmt.hu/api/publication/34607533 ID - 34607533 N1 - Export Date: 3 April 2024 Correspondence Address: Tian, Y.; Shanghai Business SchoolChina; email: yongge.tian@gmail.com AB - 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*. LA - English DB - MTMT ER - TY - GEN AU - Eyo, Eyo Ita III AU - Chopin, Soo AU - Hoi-Lai, Yu TI - Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory PY - 2021 UR - https://m2.mtmt.hu/api/publication/32085481 ID - 32085481 LA - English DB - MTMT ER - TY - JOUR AU - Roman, Marcel AU - Sandovici, Adrian TI - Adjoint to each other linear relations. Nieminen type criteria JF - MONATSHEFTE FUR MATHEMATIK J2 - MONATSH MATH PY - 2021 SN - 0026-9255 DO - 10.1007/s00605-021-01579-9 UR - https://m2.mtmt.hu/api/publication/32083562 ID - 32083562 N1 - Export Date: 7 September 2022 Correspondence Address: Sandovici, A.; Department of Mathematics and Informatics, B-dul Carol I, nr. 11, Romania; email: adrian.sandovici@luminis.ro LA - English DB - MTMT ER - TY - JOUR AU - Roman, Marcel AU - Sandovici, Adrian TI - Essentially self-adjoint linear relations in Hilbert spaces JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG VL - 83 PY - 2021 SP - 122 EP - 132 PG - 11 SN - 0031-5303 DO - 10.1007/s10998-020-00373-8 UR - https://m2.mtmt.hu/api/publication/32083559 ID - 32083559 N1 - Export Date: 7 September 2022 Correspondence Address: Sandovici, A.; Department of Mathematics and Informatics, B-dul Carol I, nr. 11, Romania; email: adrian.sandovici@tuiasi.ro LA - English DB - MTMT ER - TY - JOUR AU - Hassi, Seppo AU - Labrousse, Jean-Philippe AU - de Snoo, Henk TI - Operational calculus for rows, columns, and blocks of linear relations JF - ADVANCES IN OPERATOR THEORY J2 - ADV OPERAT THEORY VL - 5 PY - 2020 IS - 3 SP - 1193 EP - 1228 PG - 36 SN - 2538-225X DO - 10.1007/s43036-020-00085-3 UR - https://m2.mtmt.hu/api/publication/31488892 ID - 31488892 N1 - Cited By :2 Export Date: 7 September 2022 Correspondence Address: de Snoo, H.; Bernoulli Institute for Mathematics, P.O. Box 407, Netherlands; email: hsvdesnoo@gmail.com AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sandovici, Adrian TI - On the Adjoint of Linear Relations in Hilbert Spaces JF - MEDITERRANEAN JOURNAL OF MATHEMATICS J2 - MEDITERR J MATH VL - 17 PY - 2020 IS - 2 SN - 1660-5446 DO - 10.1007/s00009-020-1503-y UR - https://m2.mtmt.hu/api/publication/31325292 ID - 31325292 N1 - Cited By :5 Export Date: 7 September 2022 Correspondence Address: Sandovici, A.; Department of Mathematics and Informatics, B-dul Carol I, nr. 11, Romania; email: adrian.sandovici@luminis.ro LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Range-kernel characterizations of operators which are adjoint of each other JF - ADVANCES IN OPERATOR THEORY J2 - ADV OPERAT THEORY VL - 5 PY - 2020 IS - 3 SP - 1026 EP - 1038 PG - 13 SN - 2538-225X DO - 10.1007/s43036-020-00068-4 UR - https://m2.mtmt.hu/api/publication/31300976 ID - 31300976 N1 - Cited By :3 Export Date: 7 September 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c., Hungary; email: tarcsay@cs.elte.hu LA - English DB - MTMT ER - TY - GEN AU - Yongge, Tian TI - Two Removal and Cancellation Laws Associated with a Complex Matrix and Its Conjugate Transpose PY - 2020 UR - https://m2.mtmt.hu/api/publication/32083675 ID - 32083675 LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - On the adjoint of Hilbert space operators JF - LINEAR AND MULTILINEAR ALGEBRA J2 - LINEAR MULTILINEAR A VL - 67 PY - 2019 IS - 3 SP - 625 EP - 645 PG - 21 SN - 0308-1087 DO - 10.1080/03081087.2018.1430120 UR - https://m2.mtmt.hu/api/publication/30446535 ID - 30446535 N1 - Funding Agency and Grant Number: Hungarian Ministry of Human Capacities [NTP-NFTO-17] Funding text: Zsigmond Tarcsay was supported by the Hungarian Ministry of Human Capacities [grant number NTP-NFTO-17]. AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - On the square root of a positive selfadjoint operator JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG VL - 75 PY - 2017 IS - 2 SP - 268 EP - 272 PG - 5 SN - 0031-5303 DO - 10.1007/s10998-017-0192-1 UR - https://m2.mtmt.hu/api/publication/3293570 ID - 3293570 N1 - Cited By :7 Export Date: 7 September 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis, Pázmány Péter sétány 1/c, Hungary; email: tarcsay@cs.elte.hu AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - Adjoint of sums and products of operators in Hilbert spaces JF - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED) J2 - ACTA SCI MATH (SZEGED) VL - 82 PY - 2016 IS - 1-2 SP - 175 EP - 191 PG - 17 SN - 0001-6969 DO - 10.14232/actasm-015-809-3 UR - https://m2.mtmt.hu/api/publication/3084669 ID - 3084669 N1 - Cited By :11 Export Date: 7 September 2022 LA - English DB - MTMT ER - TY - JOUR AU - Popovici, D AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - On the sum between a closable operator T and a T-bounded operator JF - ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EÖTVÖS NOMINATAE - SECTIO MATHEMATICA J2 - ANN UNIV SCI BP R EÖTVÖS NOM SECT MATH VL - 58 PY - 2015 SP - 95 EP - 104 PG - 10 SN - 0524-9007 UR - https://m2.mtmt.hu/api/publication/3079729 ID - 3079729 LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - Characterizations of essentially self-adjoint and skew-adjoint operators JF - STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA J2 - STUD SCI MATH HUNG VL - 52 PY - 2015 IS - 3 SP - 371 EP - 385 PG - 15 SN - 0081-6906 DO - 10.1556/012.2015.52.3.1300 UR - https://m2.mtmt.hu/api/publication/2969008 ID - 2969008 N1 - Cited By :8 Export Date: 7 September 2022 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - Operators having selfadjoint squares JF - ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EÖTVÖS NOMINATAE - SECTIO MATHEMATICA J2 - ANN UNIV SCI BP R EÖTVÖS NOM SECT MATH VL - 58 PY - 2015 SP - 105 EP - 110 PG - 6 SN - 0524-9007 UR - https://m2.mtmt.hu/api/publication/3079747 ID - 3079747 LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - A reversed von Neumann theorem JF - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED) J2 - ACTA SCI MATH (SZEGED) VL - 80 PY - 2014 IS - 3-4 SP - 659 EP - 664 PG - 6 SN - 0001-6969 DO - 10.14232/actasm-013-283-x UR - https://m2.mtmt.hu/api/publication/2853826 ID - 2853826 N1 - Cited By :8 Export Date: 7 September 2022 LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond TI - Closed range positive operators on Banach spaces JF - ACTA MATHEMATICA HUNGARICA J2 - ACTA MATH HUNG VL - 142 PY - 2014 IS - 2 SP - 494 EP - 501 PG - 8 SN - 0236-5294 DO - 10.1007/s10474-013-0380-2 UR - https://m2.mtmt.hu/api/publication/2542482 ID - 2542482 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - CHARACTERIZATIONS OF SELFADJOINT OPERATORS JF - STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA J2 - STUD SCI MATH HUNG VL - 50 PY - 2013 IS - 4 SP - 423 EP - 435 PG - 13 SN - 0081-6906 DO - 10.1556/SScMath.50.2013.4.1252 UR - https://m2.mtmt.hu/api/publication/2541922 ID - 2541922 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond TI - On form sums of positive operators JF - ACTA MATHEMATICA HUNGARICA J2 - ACTA MATH HUNG VL - 140 PY - 2013 IS - 1-2 SP - 187 EP - 201 PG - 15 SN - 0236-5294 DO - 10.1007/s10474-013-0299-7 UR - https://m2.mtmt.hu/api/publication/2385712 ID - 2385712 AB - 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. LA - English DB - MTMT ER -