Finite Representability of ℓp in Quotients of Banach Spaces

Finite Representability of ℓp in Quotients of Banach Spaces A typical result of the paper states that if X is a Banach space with a basis and for some 1≤p≤q≤∞, the spaces ℓp and ℓq are finitely block representable in every block subspace of X, then every block subspace of X admits a block quotient Z such that for every rℓ[p,q], the space ℓr is finitely block representable in Z. Results of a similar nature are also established for ℓN p-block-sequences and asymptotic spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Finite Representability of ℓp in Quotients of Banach Spaces

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009834625767
Publisher site
See Article on Publisher Site

Abstract

A typical result of the paper states that if X is a Banach space with a basis and for some 1≤p≤q≤∞, the spaces ℓp and ℓq are finitely block representable in every block subspace of X, then every block subspace of X admits a block quotient Z such that for every rℓ[p,q], the space ℓr is finitely block representable in Z. Results of a similar nature are also established for ℓN p-block-sequences and asymptotic spaces.

Journal

PositivitySpringer Journals

Published: Oct 3, 2004

References

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