论文标题
无限无限的代数通用性和序列空间间隙
Uncountably infinite algebraic genericity and spaceability for sequence spaces
论文作者
论文摘要
令$ x $为复杂值序列的拓扑矢量空间，而$ y $为$ x $的子集。我们为$ x \ setMinus y \ cup \ {0 \} $提供条件，以包含无限的无限线性独立密度向量子空间$ x $。我们还提供了$ x \ setminus y \ cup \ {0 \} $的条件，以包含无限无限的许多线性独立封闭的无限维矢量子空间，为$ x $。我们将这些结果应用于包含$ \ ell^p $空间的一系列空间。
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.
