(untitled) (European Journal of Pure and Applied Mathematics, 2023)
In this note, we deal with a perfect sequence space λ and a bornological convex space E to introduce and study the space λ(E) of totally λ-summable sequences from E. We prove that λ(E) is complete if and only if λ an E are complete, nuclear if and only if λ an E are nuclear. and we make use of a result of Rolnald C. Rosier to give a similar characterization of the nuclearity of Λ{E} of all absolutely λ- summable sequences in a locally convex E.