International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 172839 | https://doi.org/10.1155/S0161171287000292

Manjul Gupta, P. K. Kamthan, " -similar bases", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 172839, 6 pages, 1987. https://doi.org/10.1155/S0161171287000292

λ-similar bases

Received01 May 1986

Abstract

Corresponding to an arbitrary sequence space λ, a sequence {xn} in a locally convex space (l.c.s.) (X,T) is said to be λ-similar to a sequence {yn} in another l.c.s. (Y,S) if for an arbitrary sequence {αn} of scalars, {αn p(xn)} ϵ λ for all p ϵ DT{αn q(yn)} ϵ λ, for all q ϵ DS, where DT and DS are respectively the family of all T and S continuous seminorms generating T and S.In this note we investigate conditions on λ and the spaces (X,T) and (Y,S) which ultimately help to characterize λ similarity between two Schauder bases. We also determine relationship of this concept with λ-bases.

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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