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arXiv · 2411.00797

On Schauder Bases in Hilbert Space

Oleg Zubelevich
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Abstract

In this short note we present a far generalization of the following very well-known assertion: assume that we have two orthonormal sequences in a Hilbert space and these sequences are quadratically close to each other. Then if one of these sequences is a basis in the Hilbert space then so is the other one.

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Oleg Zubelevich. 2024-10-19. On Schauder Bases in Hilbert Space. https://arxiv.org/abs/2411.00797

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