Approximating points of a Banach space by points of an operator image

Taras Banakh; Yuriy Golovaty

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arXiv · 1901.10726

Approximating points of a Banach space by points of an operator image

Taras Banakh·Yuriy Golovaty

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Abstract

Answering one problem that has its origins in quantum mechanics, we prove that for any sequence $(A_n)_{n\in\mathbb N}$ of convex nowhere dense sets in a Banach space $X$ and any sequence $(\varepsilon_n)_{n=1}^\infty$ of positive real numbers with $\lim_{n\to\infty}\varepsilon_n=0$, the set $A=\{x\in X:\forall n\in\mathbb N\;\exists a\in A_n\;\;\|x-a\|< \varepsilon_n\}$ is nowhere dense in $X$.

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BibTeX RIS

Taras Banakh, Yuriy Golovaty. 2019-01-30. Approximating points of a Banach space by points of an operator image. https://arxiv.org/abs/1901.10726

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