Bilinear forms, Schur multipliers, complete boundedness and duality
Functional Analysis
2023-01-13 v1 Operator Algebras
Abstract
Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. Based on the theory of operator spaces and completely bounded mappings we present norm optimal versions of these results and two norm optimal factorization results related to the Schur product. We show that the spaces of respectively bilinear forms and Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.
Cite
@article{arxiv.2301.05005,
title = {Bilinear forms, Schur multipliers, complete boundedness and duality},
author = {Erik Christensen},
journal= {arXiv preprint arXiv:2301.05005},
year = {2023}
}
Comments
A part of this was previously announced on the arXiv as the first half of the article "Norm optimal factorizations of scalar and block matrices", arXiv:2211.00591. Later results have forced a division of the article. The part on block matrices will appear separately