Matrix representations of arbitrary bounded operators on Hilbert spaces
Functional Analysis
2023-11-10 v2
Abstract
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.
Cite
@article{arxiv.2206.14266,
title = {Matrix representations of arbitrary bounded operators on Hilbert spaces},
author = {Vladimir Müller and Yuri Tomilov},
journal= {arXiv preprint arXiv:2206.14266},
year = {2023}
}
Comments
This is a version of the paper to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal)