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  - Contino, Maximiliano
AU  - Maestripieri, Alejandra
AU  - Marcantognini, Stefania
TI  - A matrix formula for Schur complements of nonnegative selfadjoint linear relations
JF  - LINEAR ALGEBRA AND ITS APPLICATIONS
J2  - LINEAR ALGEBRA APPL
VL  - 654
PY  - 2022
SP  - 143
EP  - 176
PG  - 34
SN  - 0024-3795
DO  - 10.1016/j.laa.2022.09.003
UR  - https://m2.mtmt.hu/api/publication/33218740
ID  - 33218740
AB  - If a nonnegative selfadjoint linear relation A in a Hilbert space and a closed subspace S are assumed to satisfy that the domain of A is invariant under the orthogonal projector onto S, then A admits a particular matrix representation with respect to the decomposition S circle plus S-&updatedExpOTTOM;. This matrix representation of A is used to give explicit formulae for the Schur complement of A on S as well as the S-compression of A. (c) 2022 Elsevier Inc. All rights reserved.
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  - 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  - Gesztesy, Fritz
AU  - Schmuedgen, Konrad
TI  - On a theorem of Z. Sebestyen and Zs. Tarcsay
JF  - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)
J2  - ACTA SCI MATH (SZEGED)
VL  - 85
PY  - 2019
IS  - 1-2
SP  - 291
EP  - 293
PG  - 3
SN  - 0001-6969
DO  - 10.14232/actasm-018-295-y
UR  - https://m2.mtmt.hu/api/publication/31096291
ID  - 31096291
N1  - Cited By :3            
            Export Date: 11 April 2023
AB  - We reprove a recent result of Z. Sebestyen and Zs. Tarcsay [9]: If T*T and TT* are self-adjoint, then T is closed.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hassi, Seppo
AU  - Sandovici, Adrian
AU  - de Snoo, Henk
TI  - Factorized sectorial relations, their maximal-sectorial extensions, and form sums
JF  - BANACH JOURNAL OF MATHEMATICAL ANALYSIS
J2  - BANACH J MATH ANAL
VL  - 13
PY  - 2019
IS  - 3
SP  - 538
EP  - 564
PG  - 27
SN  - 2662-2033
DO  - 10.1215/17358787-2019-0003
UR  - https://m2.mtmt.hu/api/publication/31093434
ID  - 31093434
N1  - Cited By :4            
            Export Date: 30 May 2023            
            Correspondence Address: Hassi, S.; Department of Mathematics and Statistics, P.O. Box 700, Finland; email: seppo.hassi@uwasa.fi
AB  - In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H. Our particular interest is in sectorial relations S, which can be expressed in the factorized formS = T* (I + iB)T or S = T (I + iB)T*;where B is a bounded self-adjoint operator in a Hilbert space K and T : H -> K (or T : K -> H, respectively) is a linear operator or a linear relation which is not assumed to be closed. Using the speci fi c factorized form of S, a description of all the maximal-sectorial extensions of S is given, along with a straightforward construction of the extreme extensions S-F, the Friedrichs extension, and S-K, the Krein extension of S, which uses the above factorized form of S. As an application of this construction, we also treat the form sum of maximal-sectorial extensions of two sectorial relations.
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  - GEN
AU  - Seppo, Hassi
AU  - Henk, de Snoo
TI  - A class of sectorial relations and the associated closed forms
PY  - 2019
UR  - https://m2.mtmt.hu/api/publication/31329167
ID  - 31329167
LA  - English
DB  - MTMT
ER  - 

TY  - GEN
AU  - Gesztesy, Fritz
AU  - Schmüdgen, Konrad
TI  - Some Remarks on the Operator T^* T
PY  - 2018
UR  - https://m2.mtmt.hu/api/publication/27207408
ID  - 27207408
N1  - idéző Cím: Some Remarks on the Operator T^* T
idéző Folyóirat/Könyv cím/Szabadalmi szám: arXiv preprint arXiv:1802.05793
idéző Megjelenés éve: 2018
idéző Sorozat cím: arXiv preprint arXiv:1802.05793
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  - Hassi, S
AU  - Sandovici, A
AU  - de Snoo, H S V
AU  - Winkler, H
TI  - Extremal maximal sectorial extensions of sectorial relations
JF  - INDAGATIONES MATHEMATICAE-NEW SERIES
J2  - INDAGAT MATH NEW SER
VL  - 28
PY  - 2017
IS  - 5
SP  - 1019
EP  - 1055
PG  - 37
SN  - 0019-3577
DO  - 10.1016/j.indag.2017.07.003
UR  - https://m2.mtmt.hu/api/publication/27080636
ID  - 27080636
N1  - Cited By :4            
            Export Date: 10 November 2022            
            CODEN: IMTHB            
            Correspondence Address: de Snoo, H.S.V.; Department of Mathematics and Statistics, P.O. Box 700, Finland; email: hsvdesnoo@gmail.com
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  - GEN
AU  - Hassi, Seppo
TI  - Factorization, majorization, and domination for linear relations
PY  - 2014
UR  - https://m2.mtmt.hu/api/publication/24777434
ID  - 24777434
N1  - idéző Cím: Factorization, majorization, and domination for linear relations
idéző Folyóirat/Könyv cím/Szabadalmi szám: arXiv preprint arXiv:1411.5922
idéző Megjelenés éve: 2014
idéző Sorozat cím: arXiv preprint arXiv:1411.5922
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  -