Matrix representations of arbitrary bounded operators on Hilbert spaces

0583468 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
Müller, Vladimír - Tomilov, Y.
Matrix representations of arbitrary bounded operators on Hilbert spaces.
Journal für die Reine und Angewandte Mathematik: Crelles journal. Roč. 2024, č. 808 (2024), s. 111-141. ISSN 0075-4102. E-ISSN 1435-5345
Grant CEP: GA ČR(CZ) GF20-22230L
Institucionální podpora: RVO:67985840
Klíčová slova: Hilbert space * matrix * linear operator
Obor OECD: Pure mathematics
Impakt faktor: 1.5, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1515/crelle-2023-0095

We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to interesting consequences, e.g., when the tuple consists of powers of a single operator. We also prove several variants of this result of independent interest. The paper substantially extends former research on matrix representations in infinite-dimensional spaces dealing mainly with prescribing the main diagonals.
Trvalý link: https://hdl.handle.net/11104/0351438