@article{MTMT:31488892,
author = {Hassi, Seppo and Labrousse, Jean-Philippe and de Snoo, Henk},
doi = {10.1007/s43036-020-00085-3},
title = {Operational calculus for rows, columns, and blocks of linear relations},
journal-iso = {ADV OPERAT THEORY},
journal = {ADVANCES IN OPERATOR THEORY},
volume = {5},
unique-id = {31488892},
abstract = {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.},
keywords = {PRODUCT; adjoint; Linear relation; Operator matrix; Row operator; Column operator},
year = {2020},
eissn = {2538-225X},
pages = {1193-1228}
}
@article{MTMT:31325292,
author = {Sandovici, Adrian},
doi = {10.1007/s00009-020-1503-y},
title = {On the Adjoint of Linear Relations in Hilbert Spaces},
journal-iso = {MEDITERR J MATH},
journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
volume = {17},
unique-id = {31325292},
issn = {1660-5446},
year = {2020}
}
@article{MTMT:31300976,
author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
doi = {10.1007/s43036-020-00068-4},
title = {Range-kernel characterizations of operators which are adjoint of each other},
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:30440374,
author = {Sandovici, Adrian},
doi = {10.1016/j.jmaa.2018.09.063},
title = {Self-adjointness and skew-adjointness criteria involving powers of linear relations},
journal-iso = {J MATH ANAL APPL},
journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
volume = {470},
unique-id = {30440374},
issn = {0022-247X},
abstract = {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.},
keywords = {Hilbert space; Symmetric linear relation; Nonnegative linear relation; Selfadjoint linear relation; Skew-symmetric linear relation; Skew-adjoint linear relation},
year = {2019},
eissn = {1096-0813},
pages = {186-200}
}
@article{MTMT:30446535,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
doi = {10.1080/03081087.2018.1430120},
title = {On the adjoint of Hilbert space operators},
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:30440476,
author = {Corso, Rosario},
doi = {10.1007/s11785-018-0805-6},
title = {Maximal Operators with Respect to the Numerical Range},
journal-iso = {COMPLEX ANAL OPER TH},
journal = {COMPLEX ANALYSIS AND OPERATOR THEORY},
unique-id = {30440476},
issn = {1661-8254},
abstract = {Let $$\\mathfrak {n}$$nbe a nonempty, proper, convex subset of $$\\mathbb {C}$$C. The $$\\mathfrak {n}$$n-maximal operators are defined as the operators having numerical ranges in $$\\mathfrak {n}$$nand are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $$\\mathfrak {n}$$n-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.},
year = {2018},
eissn = {1661-8262},
pages = {1}
}
@article{MTMT:30440389,
author = {Sandovici, A.},
doi = {10.1007/s10474-018-0883-y},
title = {A range matrix-type criterion for the self-adjointness of symmetric linear relations},
journal-iso = {ACTA MATH HUNG},
journal = {ACTA MATHEMATICA HUNGARICA},
unique-id = {30440389},
issn = {0236-5294},
abstract = {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.},
year = {2018},
eissn = {1588-2632},
pages = {1}
}
@article{MTMT:27565733,
author = {Sandovici, Adrian},
doi = {10.1080/03081087.2017.1369930},
title = {Von Neumann's theorem for linear relations},
journal-iso = {LINEAR MULTILINEAR A},
journal = {LINEAR AND MULTILINEAR ALGEBRA},
volume = {66},
unique-id = {27565733},
issn = {0308-1087},
year = {2018},
eissn = {1563-5139},
pages = {1750-1756}
}
@article{MTMT:27207403,
author = {Sandovici, Adrian},
doi = {10.1080/03081087.2017.1295432},
title = {Von Neumann’s theorem for linear relations},
journal-iso = {LINEAR MULTILINEAR A},
journal = {LINEAR AND MULTILINEAR ALGEBRA},
volume = {2017},
unique-id = {27207403},
issn = {0308-1087},
year = {2017},
eissn = {1563-5139},
pages = {1-7}
}
@article{MTMT:3293570,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
doi = {10.1007/s10998-017-0192-1},
title = {On the square root of a positive selfadjoint operator},
journal-iso = {PERIOD MATH HUNG},
journal = {PERIODICA MATHEMATICA HUNGARICA},
volume = {75},
unique-id = {3293570},
issn = {0031-5303},
abstract = {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.},
keywords = {SQUARE ROOT; Positive operator; selfadjoint operator; Unbounded operator},
year = {2017},
eissn = {1588-2829},
pages = {268-272},
orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}
@misc{MTMT:26333739,
author = {Hirasawa, G},
doi = {10.14232/actasm-015-044-4},
title = {Selfadjoint operators and symmetric operators},
unique-id = {26333739},
year = {2016},
pages = {529-543}
}
@article{MTMT:3084669,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
doi = {10.14232/actasm-015-809-3},
title = {Adjoint of sums and products of operators in Hilbert spaces},
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:3079729,
author = {Popovici, D and Sebestyén, Zoltán and Tarcsay, Zsigmond},
title = {On the sum between a closable operator T and a T-bounded operator},
journal-iso = {ANN UNIV SCI BP R EÖTVÖS NOM SECT MATH},
journal = {ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EÖTVÖS NOMINATAE - SECTIO MATHEMATICA},
volume = {58},
unique-id = {3079729},
issn = {0524-9007},
year = {2015},
pages = {95-104},
orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}
@article{MTMT:2969008,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
doi = {10.1556/012.2015.52.3.1300},
title = {Characterizations of essentially self-adjoint and skew-adjoint operators},
journal-iso = {STUD SCI MATH HUNG},
journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA},
volume = {52},
unique-id = {2969008},
issn = {0081-6906},
abstract = {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.},
keywords = {Symmetric operators; Skewadjoint operators; Skew-symmetric operators; Essentially selfadjoint operators},
year = {2015},
eissn = {1588-2896},
pages = {371-385},
orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}
@article{MTMT:3079747,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
title = {Operators having selfadjoint squares},
journal-iso = {ANN UNIV SCI BP R EÖTVÖS NOM SECT MATH},
journal = {ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EÖTVÖS NOMINATAE - SECTIO MATHEMATICA},
volume = {58},
unique-id = {3079747},
issn = {0524-9007},
year = {2015},
pages = {105-110},
orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}
@article{MTMT:2853826,
author = {Sebestyén, Zoltán and Tarcsay, Zsigmond},
doi = {10.14232/actasm-013-283-x},
title = {A reversed von Neumann theorem},
journal-iso = {ACTA SCI MATH (SZEGED)},
journal = {ACTA SCIENTIARUM MATHEMATICARUM - SZEGED},
volume = {80},
unique-id = {2853826},
issn = {0001-6969},
year = {2014},
pages = {659-664},
orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}