Original Articles

There is No Lattice Preserving Natural Tensor Norm

Published in: Quaestiones Mathematicae
Volume 27 , issue 3 , 2004 , pages: 267–273

DOI: 10.2989/16073600409486099

Author(s): Pérez-García , Ignacio Villanueva

Keywords: BANACH LATTICES , UNCONDITIONAL BASIS , TENSOR PRODUCTS , MULTILINEAR OPERATORS

Abstract

We prove that for every natural tensor norm α, one can find a Banach lattice X such that the tensor product X ⊗ X endowed with the norm α does not have the Gordon-Lewis property and, therefore, cannot be isomorphic to any Banach lattice. We also discuss the situation for arbitrary tensor norms.

« Riesz Reasonable Cross Norms on Tensor Products of Banach Lattices

Separation of Convex Sets and Best Approximation in Spaces with Asymmetric Norm »