Characterizations of almost shrinking bases
Abstract
The material of this paper depends upon the theory of locally convex spaces, sequence spaces and Schauder bases in topological vector spaces and as such we refer to [2] (cf. also [9]), [6] and [7] respectively for several unexpalined definitions, results and terms prevalent in the sequel.However, we do recall a few definitions and terms relevant to the present paper. So, we write thorughout 
for an arbitrary Hausdorff locally convex space (l.c.s.) with 
denoting the topological dual of X and 
representing the saturated collection of all T-continuous seminorms generating the locally convex (l.c) topology T on X.Also we write the pair of sequences 
for an arbitrary Schauder basis (S.b.) for X where 
and 
An S.b. 
for 
is called shrinking if 
is an S.b. for the strong dual 
being the usual canonical embedding from X into(Error rendering LaTeX formula)
for an arbitrary Hausdorff locally convex space (l.c.s.) with denoting the topological dual of X and representing the saturated collection of all T-continuous seminorms generating the locally convex (l.c) topology T on X.Also we write the pair of sequences for an arbitrary Schauder basis (S.b.) for X where and An S.b. for is called shrinking if is an S.b. for the strong dual being the usual canonical embedding from X into(Error rendering LaTeX formula)DOI Code:
10.1285/i15900932v10n1p67
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