λ -similar bases

Manjul Gupta and P. K. Kamthan

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-6

Abstract:

Corresponding to an arbitrary sequence space λ , a sequence { x n } in a locally convex space (l.c.s.) ( X , T ) is said to be λ -similar to a sequence { y n } in another l.c.s. ( Y , S ) if for an arbitrary sequence { α n } of scalars, { α n p ( x n ) } ϵ λ for all p ϵ D T ⇔ { α n q ( y n ) } ϵ λ , for all q ϵ D S , where D T and D S 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.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:172839

DOI: 10.1155/S0161171287000292

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