2022/06/28 by Yuri Tomilov, Müller, Vladimir, Tomilov, Yuri · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Topics in Algebra #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2206.14266
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.