Applications of a decomposition inX⊗λ Y

A Schauder Decomposition inX⊗λ when Y has a Schauder Decomposition is presented. This decomposition is then used to investigate the Approximation Property. For instance, it is shown that if X has the Approximation Property and Y has a basis thenX⊗λ has the Approximation Property. We also use this to...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata Vol. 179; no. 1; pp. 189 - 196
Main Authors: Bator, Elizabeth M., Slavens, Dawn R.
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.12.2001
Subjects:
Approximation
Continuity (mathematics)
Decomposition
Function space
Mathematical analysis
Operators (mathematics)
ISSN:0373-3114, 1618-1891
Online Access:Get full text
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Summary:A Schauder Decomposition inX⊗λ when Y has a Schauder Decomposition is presented. This decomposition is then used to investigate the Approximation Property. For instance, it is shown that if X has the Approximation Property and Y has a basis thenX⊗λ has the Approximation Property. We also use this to obtain results concerning operators on vector valued continuous function spaces.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0373-3114
1618-1891
DOI:10.1007/BF02505954