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  - 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  - Popovici, Dan
AU  - Sebestyén, Zoltán
TI  - On operators which are adjoint to each other
JF  - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)
J2  - ACTA SCI MATH (SZEGED)
VL  - 80
PY  - 2014
IS  - 1-2
SP  - 175
EP  - 194
PG  - 20
SN  - 0001-6969
DO  - 10.14232/actasm-012-857-7
UR  - https://m2.mtmt.hu/api/publication/3079525
ID  - 3079525
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  - 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  -