TY - JOUR
AU - Sidaty, Mohamed Ahmed
PY - 2023/07/30
Y2 - 2023/12/07
TI - Nuclearity of a Class of Vector-valued Sequence Spaces
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 3
SE -
DO - 10.29020/nybg.ejpam.v16i3.4831
UR - https://ejpam.com/index.php/ejpam/article/view/4831
SP - 1762-1771
AB - <p>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 $E$.</p>
ER -