Nuclearity of a Class of Vector-valued Sequence Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i3.4831Keywords:
sequence spaces, locally convex sequence spaces, nuclearity, summability, convex bornologyAbstract
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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