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.
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
