Shrinking Schauder Frames and Their Associated Bases

For a Banach space X with a shrinking Schauder frame ( x i , f i ) we provide an explicit method for constructing a shrinking associated basis. In the case that the minimal associated basis is not shrinking, we prove that every shrinking associated basis of ( x i , f i ) dominates an uncountable fam...

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Bibliographic Details
Published in:Constructive approximation 2024-12, Vol.60 (3), p.443-461
Main Authors: Beanland, Kevin, Freeman, Daniel
Format: Article
Language:English
Subjects:
Analysis
Banach spaces
Mathematics
Mathematics and Statistics
Numerical Analysis
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Summary:For a Banach space X with a shrinking Schauder frame ( x i , f i ) we provide an explicit method for constructing a shrinking associated basis. In the case that the minimal associated basis is not shrinking, we prove that every shrinking associated basis of ( x i , f i ) dominates an uncountable family of incomparable shrinking associated bases of ( x i , f i ) . By adapting a construction of Pełczyński, we characterize spaces with shrinking Schauder frames as space having the w ∗ -bounded approximation property.
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-023-09667-9