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arXiv · 2211.04541

Uncountably infinite algebraic genericity and spaceability for sequence spaces

C. A. Konidas
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Abstract

Let $X$ be a topological vector space of complex-valued sequences and $Y$ be a subset of $X$. We provide conditions for $X \setminus Y \cup \{0\}$ to contain uncountably infinitely many linearly independent dense vector subspaces of $X$. We also provide conditions for $X \setminus Y \cup \{0\}$ to contain uncountably infinitely many linearly independent closed infinite-dimensional vector subspaces of $X$. We apply these results to a chain of spaces containing the $\ell^p$ spaces.

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C. A. Konidas. 2022-11-08. Uncountably infinite algebraic genericity and spaceability for sequence spaces. https://arxiv.org/abs/2211.04541

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