On unboundedness of natural projectors in spaces of infinite matrices
https://doi.org/10.67268/1812-5093-2026-34-1-45-55
EDN: ETIXQP
Abstract
In this paper, we consider Banach spaces of operators from $\ell^p$ to $\ell^q$ that can be realized as infinite matrices. We show that for $p>1$ and $q<\infty$, for almost all subspaces formed by randomly chosen matrix units, the canonical projectors onto these subspaces will be unbounded. Moreover, these projectors will be unbounded even on the class of matrices with elements $a_{ij}\in\{-1,0,1\}$.
About the Authors
V. N. Kunica
Belarusian State University
Belarus
Belarus
Minsk
K. V. Lykov
Institute of Mathematics of the National Academy of Sciences of Belarus;
Belarusian State University
Belarus
Belarus
Minsk
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Review
For citations:
Kunica V.N., Lykov K.V. On unboundedness of natural projectors in spaces of infinite matrices. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):45-55. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1-45-55. EDN: ETIXQP
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