Turkish Journal of Mathematics
DOI
10.3906/mat-1506-44
Abstract
Let $\mathbb{F}^\mathbb{N}$ denote the vector space of all scalar sequences. If $A$ is an infinite matrix with nonnegative entries and $\lambda$ is a solid subspace of $\mathbb{F}^\mathbb{N}$, then $ sol-A^{-1}(\lambda)=\{x\in \mathbb{F}^\mathbb{N} : A x \in \lambda\} $ is also a solid subspace of $\mathbb{F}^\mathbb{N}$ that, under certain conditions on $A$ and $\lambda$, inherits a solid topological vector space topology from any such topology on $\lambda$. Letting $\Lambda_0=\lambda$ and $\Lambda_m=sol-A^{-1}(\Lambda_{m-1})$ for $m>0$, we derive an infinite sequence $\Lambda_0, \Lambda_1, \Lambda_2,...$ of solid subspaces of $\mathbb{F}^\mathbb{N}$ from the inputs $A$ and $\lambda$. For $A$ and $\lambda$ confined to certain classes, we ask many questions about this derived sequence and answer a few.
Keywords
Solid sequence space, Toeplitz matrix, projective limit, solid topology
First Page
1025
Last Page
1037
Recommended Citation
JOHNSON, PETER D. and POLAT, FARUK
(2016)
"Problems in matricially derived solid Banach sequence spaces,"
Turkish Journal of Mathematics: Vol. 40:
No.
5, Article 9.
https://doi.org/10.3906/mat-1506-44
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss5/9
