TY - JOUR AU - Alshammari, Bader AU - Welters, Aaron TI - On the spectral theory of linear differential-algebraic equations with periodic coefficients JF - ANALYSIS AND MATHEMATICAL PHYSICS J2 - ANAL MATH PHYS VL - 13 PY - 2023 IS - 6 PG - 35 SN - 1664-2368 DO - 10.1007/s13324-023-00856-0 UR - https://m2.mtmt.hu/api/publication/34636547 ID - 34636547 LA - English DB - MTMT ER - TY - JOUR AU - Ammar, Aymen AU - Lazrag, Nawrez TI - Some results concerning the linear relations which are adjoint to each other JF - RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO J2 - REND CIRC MATEM PALERMO PY - 2023 PG - 16 SN - 0009-725X DO - 10.1007/s12215-023-00877-5 UR - https://m2.mtmt.hu/api/publication/33933786 ID - 33933786 AB - In order to study the stability of self-adjointness of a block linear relation matrix with unbounded entries acting in Hilbert spaces, we start by discussing the question whether a linear relation is identical with the adjoint of another linear relation. After that, based on the assumptions obtained, we provide other necessary and sufficient conditions about the entries for a linear relation matrix to be self-adjoint. Our results generalize one of the most important known results in the literature that works on the self-adjointness for linear relations (see Shi et al. in Linear Algebra Appl 438(1):191-218, 2013, Linear Multilinear Algebra 66(2):309-333, 2018; Shi and Xu in Linear Algebra Appl 531:547-574, 2017). LA - English DB - MTMT ER - TY - JOUR AU - Dehimi, Souheyb AU - Mortad, Mohammed Hichem TI - Unbounded operators having self-adjoint, subnormal, or hyponormal powers JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 296 PY - 2023 IS - 9 SP - 3915 EP - 3928 PG - 14 SN - 0025-584X DO - 10.1002/mana.202100390 UR - https://m2.mtmt.hu/api/publication/34272303 ID - 34272303 N1 - Cited By :1 Export Date: 3 April 2024 Correspondence Address: Mortad, M.H.; Département de Mathématiques, Université Oran 1, Ahmed Ben Bella, B.P. 1524, El Menouar, Algeria; email: mhmortad@gmail.com AB - 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. 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 - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - Extensions of positive symmetric operators and Krein's uniqueness criteria JF - LINEAR AND MULTILINEAR ALGEBRA J2 - LINEAR MULTILINEAR A PY - 2023 SN - 0308-1087 DO - 10.1080/03081087.2023.2196610 UR - https://m2.mtmt.hu/api/publication/33766588 ID - 33766588 N1 - Export Date: 11 September 2023 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c, Hungary; email: zsigmond.tarcsay@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Abdulwahid, Elaf S. TI - The class of S-operators on Hilbert space JF - JOURNAL OF INTERDISCIPLINARY MATHEMATICS J2 - J INTERDISCIP MATH VL - 25 PY - 2022 IS - 5 SP - 1401 EP - 1407 PG - 7 SN - 0972-0502 DO - 10.1080/09720502.2022.2046335 UR - https://m2.mtmt.hu/api/publication/33408001 ID - 33408001 AB - The aim of this research is to introduce a new type of operator on Hilbert space which is called S - operator. The operator T is an element of B(H) namely S - operator if (TT)-T-2*(2) + T*(2) T-2 = = 2TT*(2) T, where T* adjoint operator of T.Thus some properties of the class of S - operator are studied and relation between this class with some types operator. LA - English DB - MTMT ER - TY - JOUR AU - Elaf, S. Abdulwahid TI - The class of D(T)–operators on Hilbert spaces JF - INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS J2 - INT J NONL ANAL AND APPL VL - 12 PY - 2021 SP - 1293 EP - 1298 PG - 6 SN - 2008-6822 DO - 10.22075/ijnaa.2021.5645 UR - https://m2.mtmt.hu/api/publication/32466943 ID - 32466943 N1 - Export Date: 5 April 2023 Correspondence Address: Abdulwahid, E.S.; Department of Mathematics, Iraq; email: elafs.math@tu.edu.iq 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 - 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 - Tarcsay, Zsigmond AU - Titkos, Tamás TI - Operators on anti-dual pairs: Generalized Krein-von Neumann extension JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 294 PY - 2021 IS - 9 SP - 1821 EP - 1838 PG - 18 SN - 0025-584X DO - 10.1002/mana.201800431 UR - https://m2.mtmt.hu/api/publication/32163878 ID - 32163878 N1 - Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, H-1053, Hungary BBS University of Applied Sciences, Alkotmány u. 9, Budapest, H-1054, Hungary Export Date: 4 July 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c., Hungary; email: tarcsay@cs.elte.hu AB - The main aim of this paper is to generalize the classical concept of a positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The concept of anti-duality carries an adequate structure to define positivity in a natural way, and is still general enough to cover numerous important areas where the Hilbert space theory cannot be applied. Our running example - illustrating the applicability of the general setting to spaces bearing poor geometrical features - comes from noncommutative integration theory. Namely, representable extension of linear functionals of involutive algebras will be governed by their induced operators. The main theorem, to which the vast majority of the results is built, gives a complete and constructive characterization of those operators that admit a continuous positive extension to the whole space. Various properties such as commutation, or minimality and maximality of special extensions will be studied in detail. 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 - Roman, Marcel AU - Sandovici, Adrian TI - Multivalued Linear Operator Equation A^{*}A = \lambda A^{n} JF - COMPLEX ANALYSIS AND OPERATOR THEORY J2 - COMPLEX ANAL OPER TH VL - 15 PY - 2020 IS - 1 SN - 1661-8254 DO - 10.1007/s11785-020-01045-8 UR - https://m2.mtmt.hu/api/publication/32086186 ID - 32086186 N1 - Cited By :1 Export Date: 5 April 2023 Correspondence Address: Sandovici, A.; Department of Mathematics and Informatics, B-dul Carol I, nr. 11, Romania; email: adrian.sandovici@gmail.com 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 - GEN AU - Souheyb, Dehimi AU - Mohammed, Hichem Mortad TI - Unbounded operators having self-adjoint or normal powers and some related results PY - 2020 UR - https://m2.mtmt.hu/api/publication/32083554 ID - 32083554 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 -