International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 227-232

λ-similar bases

Manjul Gupta and P. K. Kamthan

Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India

Received 1 May 1986

Copyright © 1987 Manjul Gupta and P. K. Kamthan. 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.


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.