1998/12/30 by Peter G. Casazza, Casazza, Peter G., N. J. Nielsen +1
Mathematics · #46B40 #46B42 #Advanced Banach Space Theory #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B40 #msc:46B42
paper · pdf · doi:10.48550/arxiv.math/9812160
32 pages, latex2e
arxiv created 1998/12/30 · openalex publication_date 1998/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we first show that if X is a Banach space and α is a left invariant crossnorm on ℓ_∞⊗ X, then there is a Banach lattice L and an isometric embedding J of X into L, so that I⊗ J becomes an isometry of ℓ_∞⊗αX onto ℓ_∞⊗m J(X). Here I denotes the identity operator on ℓ_∞ and ℓ_∞⊗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 This result is originally due to G. Pisier (unpublished), but our proof is different.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 characterize the Gordon-Lewis property \GL in terms of embeddings into Banach lattices. Also other structures related to the \GL are investigated.