International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 227-232
doi:10.1155/S0161171287000292

λ-similar bases

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.