On the interplay between operators, bases, and matrices

0544170 - MÚ 2022 RIV US eng J - Journal Article
Müller, Vladimír - Tomilov, Y.
On the interplay between operators, bases, and matrices.
Journal of Functional Analysis. Roč. 281, č. 9 (2021), č. článku 109158. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : bases * diagonals * Hilbert space operators * matrix representations
OECD category: Pure mathematics
Impact factor: 1.891, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.jfa.2021.109158

Given a bounded linear operator T on a separable Hilbert space, we develop an approach allowing one to construct a matrix representation for T having certain specified algebraic or asymptotic structure. We obtain matrix representations for T with preassigned bands of the main diagonals, with an upper bound for all of the matrix elements, and with entrywise rational-like lower and upper bounds for these elements. In particular, we substantially generalize and complement our results on diagonals of operators from [47] and other related results. Moreover, we obtain a vast generalization of a theorem by Stout (1981) [56], and (partially) answer his open question. Several of our results have no analogues in the literature.
Permanent Link: http://hdl.handle.net/11104/0321220