Nuclearity of a Class of Vector-valued Sequence Spaces

Authors

  • Mohamed Ahmed Sidaty Al Imam Muhammad Ibn Saud Islamic University

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4831

Keywords:

sequence spaces, locally convex sequence spaces, nuclearity, summability, convex bornology

Abstract

In this note, we deal with a perfect sequence space $\lambda$ and a bornological convex space $E$ to introduce and study the space $\lambda(E)$ of totally $\lambda$-summable sequences from $E$. We prove that $\lambda(E)$ is complete if and only if $\lambda$ an $E$ are complete, nuclear if and only if $\lambda$ an $E$ are nuclear. and we make use of a result of Rolnald C. Rosier to give a similar characterization of the nuclearity of $\Lambda\{E\}$ of all absolutely $\lambda-$ summable sequences in a locally convex $E$.

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

Nuclearity of a Class of Vector-valued Sequence Spaces. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1762-1771. https://doi.org/10.29020/nybg.ejpam.v16i3.4831