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  - 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  - 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, 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  - 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  - Hassi, S
AU  - Sebestyén, Zoltán
AU  - De Snoo, HSV
AU  - Szafraniec, FH
TI  - A canonical decomposition for linear operators and linear relations
JF  - ACTA MATHEMATICA HUNGARICA
J2  - ACTA MATH HUNG
VL  - 115
PY  - 2007
IS  - 4
SP  - 281
EP  - 307
PG  - 27
SN  - 0236-5294
DO  - 10.1007/s10474-007-5247-y
UR  - https://m2.mtmt.hu/api/publication/2385734
ID  - 2385734
N1  - Cited By :30            
            Export Date: 4 July 2022            
            Correspondence Address: Hassi, S.; Department of Mathematics and Statistics, P.O. Box 700, 65101 Vaasa, Finland; email: sha@uwasa.fi
AB  - An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone's characteristic projection onto the closure of the linear relation. © Springer-Verlag/Akadémiai Kiadó 2007.
LA  - English
DB  - MTMT
ER  -