Uncountably infinite algebraic genericity and spaceability for sequence spaces

2022/11/08 by Konidas, C. A.
#15A03 #46A11 #46A13 #46A45 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.04541

Abstract

Let X be a topological vector space of complex-valued sequences and Y be a subset of X. We provide conditions for X ∖ Y ∪ \0\ to contain uncountably infinitely many linearly independent dense vector subspaces of X. We also provide conditions for X ∖ Y ∪ \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 ℓ^p spaces.

Related

• Topological and algebraic genericity and spaceability for an extended chain of sequence spaces
• Basic sequences and spaceability in ℓ_p spaces
• A project about chains of spaces, regarding topological and algebraic\n genericity and spaceability
• Spaceability of sets of non-injective maps
• Infinite Lineability: On the Abundance of Dense Subspaces