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A Note on Unconditional Bases

Published online by Cambridge University Press:  20 November 2018

J. R. Holub  and
J. R. Retherford
J. R. Holub
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
J. R. Retherford
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
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A sequence (xi) in a Banach space X is a Schauder basis for X provided for each x∊X there is a unique sequence of scalars (ai) such that

1.1

convergence in the norm topology. It is well known [1] that if (xi) is a (Schauder) basis for X and (fi) is defined by

1.2

where then fi(xj) = δij and fi∊X* for each positive integer i.

A sequence (xi) is a éasic sequence in X if (xi) is a basis for [xi], where the bracketed expression denotes the closed linear span of (xi).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 369 - 372
Copyright
Copyright © Canadian Mathematical Society 1972

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