ArticleOriginal scientific text

Title

Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis

Authors 1

Affiliations

  1. Dipartimento di Matematica del Politecnico, Piazza Leonardo da Vinci, 32 20133 Milano, Italy

Abstract

Every separable, infinite-dimensional Banach space X has a biorthogonal sequence {zn,zn}, with span{zn} norming on X and {zn+zn} bounded, so that, for every x in X and x* in X*, there exists a permutation {π(n)} of {n} so that xconv¯{finite subseries of n=1zn(x)zn}andxn(x)=n=1zπ(n)(x)x(zπ(n)).

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Pages:
207-222
Main language of publication
English
Received
1990-12-01
Accepted
1991-12-06
Published
1994
Exact and natural sciences