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.
Funding statement: The first author was supported by grant No. 20-22230L of GA CR and RVO: 67985840. The second author was partially supported by NCN grant UMO-2017/27/B/ST1/00078.
Acknowledgements
We would like to thank the referee for pertinent comments and remarks that led to improvement of this paper.
References
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