Embeddings of Banach spaces into Banach lattices and the Gordon-Lewis property

In this paper we first show that if X is a Banach space and [alpha] is a left invariant crossnorm on [cursive l][infinity][x in circle]X, then there is a Banach lattice L and an isometric embedding J of X into L, so that I [x in circle] J becomes an isometry of [cursive l][infinity][x in circle][alp...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2001-12, Vol.5 (4), p.297-321
Main Authors: CASAZZA, P. G, NIELSEN, N. J
Format: Article
Language:English
Subjects:
Banach spaces
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Sciences and techniques of general use
Online Access:Get full text
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Summary:In this paper we first show that if X is a Banach space and [alpha] is a left invariant crossnorm on [cursive l][infinity][x in circle]X, then there is a Banach lattice L and an isometric embedding J of X into L, so that I [x in circle] J becomes an isometry of [cursive l][infinity][x in circle][alpha]X onto [cursive l][infinity][x in circle]m J(X). Here I denotes the identity operator on [cursive l][infinity] and [cursive l][infinity][x in circle]m J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon-Lewis property GL and related structures in terms of embeddings into Banach lattices. [PUBLICATION ABSTRACT]
ISSN:1385-1292
1572-9281
DOI:10.1023/A:1011845208065