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 - JOUR AU - Mortad, M.H. TI - Certain properties involving the unbounded operators p(T), TT⁎, and T⁎T; and some applications to powers and nth roots of unbounded operators JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 525 PY - 2023 IS - 2 SN - 0022-247X DO - 10.1016/j.jmaa.2023.127159 UR - https://m2.mtmt.hu/api/publication/33735457 ID - 33735457 N1 - Export Date: 5 April 2023 Funding text 1: The author wishes to thank Professor Zsigmond Tarcsay for Example 8.5, which was based on a construction by Z. Sebestyén and J. Stochel (see [65]). AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Berkics, Péter TI - On Self-Adjoint Linear Relations JF - MATHEMATICA PANNONICA J2 - MATH PANNONICA VL - 27_NS1 PY - 2021 IS - 1 SP - 1 EP - 7 PG - 7 SN - 0865-2090 DO - 10.1556/314.2020.00001 UR - https://m2.mtmt.hu/api/publication/32083667 ID - 32083667 LA - English DB - MTMT ER - TY - JOUR AU - Ita, Eyo Eyo III AU - Soo, Chopin AU - Yu, Hoi Lai TI - Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory JF - CLASSICAL AND QUANTUM GRAVITY J2 - CLASSICAL QUANT GRAV VL - 38 PY - 2021 IS - 3 PG - 12 SN - 0264-9381 DO - 10.1088/1361-6382/abcb0e UR - https://m2.mtmt.hu/api/publication/32381366 ID - 32381366 N1 - Export Date: 7 September 2022 Correspondence Address: Soo, C.; Department of Physics, Taiwan; email: cpsoo@mail.ncku.edu.tw AB - 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. 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 - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Canonical Graph Contractions of Linear Relations on Hilbert Spaces JF - COMPLEX ANALYSIS AND OPERATOR THEORY J2 - COMPLEX ANAL OPER TH VL - 15 PY - 2021 IS - 1 SN - 1661-8254 DO - 10.1007/s11785-020-01066-3 UR - https://m2.mtmt.hu/api/publication/31840162 ID - 31840162 N1 - 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 - 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 - Corso, Rosario TI - Maximal Operators with Respect to the Numerical Range JF - COMPLEX ANALYSIS AND OPERATOR THEORY J2 - COMPLEX ANAL OPER TH VL - 13 PY - 2019 IS - 3 SP - 781 EP - 800 PG - 20 SN - 1661-8254 DO - 10.1007/s11785-018-0805-6 UR - https://m2.mtmt.hu/api/publication/30440476 ID - 30440476 N1 - Cited By :2 Export Date: 7 September 2022 Correspondence Address: Corso, R.; Dipartimento di Matematica e Informatica, Via Archirafi 34, Italy; email: rosario.corso@studium.unict.it AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sandovici, A. TI - A range matrix-type criterion for the self-adjointness of symmetric linear relations JF - ACTA MATHEMATICA HUNGARICA J2 - ACTA MATH HUNG VL - 158 PY - 2019 SP - 27 EP - 35 PG - 9 SN - 0236-5294 DO - 10.1007/s10474-018-0883-y UR - https://m2.mtmt.hu/api/publication/30440389 ID - 30440389 N1 - Cited By :2 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 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sandovici, Adrian TI - Self-adjointness and skew-adjointness criteria involving powers of linear relations JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 470 PY - 2019 IS - 1 SP - 186 EP - 200 PG - 15 SN - 0022-247X DO - 10.1016/j.jmaa.2018.09.063 UR - https://m2.mtmt.hu/api/publication/30440374 ID - 30440374 AB - 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. 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 - Sandovici, Adrian TI - Von Neumann's theorem for linear relations JF - LINEAR AND MULTILINEAR ALGEBRA J2 - LINEAR MULTILINEAR A VL - 66 PY - 2018 IS - 9 SP - 1750 EP - 1756 PG - 7 SN - 0308-1087 DO - 10.1080/03081087.2017.1369930 UR - https://m2.mtmt.hu/api/publication/27565733 ID - 27565733 N1 - Cited By :9 Export Date: 7 September 2022 Correspondence Address: Sandovici, A.; Department of Mathematics and Informatics, Romania; email: adrian.sandovici@luminis.ro 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 - Hirasawa, G TI - Selfadjoint operators and symmetric operators JF - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED) J2 - ACTA SCI MATH (SZEGED) VL - 82 PY - 2016 IS - 3-4 SP - 529 EP - 543 PG - 15 SN - 0001-6969 DO - 10.14232/actasm-015-044-4 UR - https://m2.mtmt.hu/api/publication/26333739 ID - 26333739 N1 - Export Date: 7 September 2022 Correspondence Address: Hirasawa, G.; Ibaraki University, 4-12-1 Nakanarusawa, Japan; email: gou.hirasawa.529@vc.ibaraki.ac.jp 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 -