@article{MTMT:31300976,
	title = {Range-kernel characterizations of operators which are adjoint of each other},
	url = {https://m2.mtmt.hu/api/publication/31300976},
	author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
	doi = {10.1007/s43036-020-00068-4},
	journal-iso = {ADV OPERAT THEORY},
	journal = {ADVANCES IN OPERATOR THEORY},
	volume = {5},
	unique-id = {31300976},
	year = {2020},
	eissn = {2538-225X},
	pages = {1026-1038},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:30446535,
	title = {On the adjoint of Hilbert space operators},
	url = {https://m2.mtmt.hu/api/publication/30446535},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1080/03081087.2018.1430120},
	journal-iso = {LINEAR MULTILINEAR A},
	journal = {LINEAR AND MULTILINEAR ALGEBRA},
	volume = {67},
	unique-id = {30446535},
	issn = {0308-1087},
	abstract = {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.},
	keywords = {Positive operator; selfadjoint operator; adjoint; closed operator},
	year = {2019},
	eissn = {1563-5139},
	pages = {625-645},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:3084669,
	title = {Adjoint of sums and products of operators in Hilbert spaces},
	url = {https://m2.mtmt.hu/api/publication/3084669},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.14232/actasm-015-809-3},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {82},
	unique-id = {3084669},
	issn = {0001-6969},
	year = {2016},
	pages = {175-191},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:3079525,
	title = {On operators which are adjoint to each other},
	url = {https://m2.mtmt.hu/api/publication/3079525},
	author = {Popovici, Dan and Sebestyén, Zoltán},
	doi = {10.14232/actasm-012-857-7},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {80},
	unique-id = {3079525},
	issn = {0001-6969},
	year = {2014},
	pages = {175-194}
}

@article{MTMT:2541922,
	title = {CHARACTERIZATIONS OF SELFADJOINT OPERATORS},
	url = {https://m2.mtmt.hu/api/publication/2541922},
	author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
	doi = {10.1556/SScMath.50.2013.4.1252},
	journal-iso = {STUD SCI MATH HUNG},
	journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
	volume = {50},
	unique-id = {2541922},
	issn = {0081-6906},
	abstract = {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.},
	keywords = {characterization; PERTURBATION; Positive operator; HILBERT-SPACE; selfadjoint operator; Symmetric operator},
	year = {2013},
	eissn = {1588-2896},
	pages = {423-435},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:2385734,
	title = {A canonical decomposition for linear operators and linear relations},
	url = {https://m2.mtmt.hu/api/publication/2385734},
	author = {Hassi, S and Sebestyén, Zoltán and De Snoo, HSV and Szafraniec, FH},
	doi = {10.1007/s10474-007-5247-y},
	journal-iso = {ACTA MATH HUNG},
	journal = {ACTA MATHEMATICA HUNGARICA},
	volume = {115},
	unique-id = {2385734},
	issn = {0236-5294},
	abstract = {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.},
	keywords = {GRAPH; closable operator; Stone decomposition; Singular relation; Relation; Regular relation; Multivalued operator; Adjoint relation},
	year = {2007},
	eissn = {1588-2632},
	pages = {281-307}
}