Matrix representations of arbitrary bounded operators on Hilbert spaces

0583468 - MÚ 2025 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Hilbert space * matrix * linear operator
OECD category: Pure mathematics
Impact factor: 1.5, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0351438