Bilinear forms, Schur multipliers, complete boundedness and duality

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Grothendieck’s inequalities for operators and bilinear forms imply some factorization results for complex m × n matrices. Based on the theory of operator spaces and completely bounded maps 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 bilinear forms and of Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.

TidsskriftMathematica Scandinavica
Udgave nummer3
Sider (fra-til)543-569
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
We are happy to thank Narutaka Ozawa, Vern Paulsen and Gilles Pisier for very valuable help and comments.

Publisher Copyright:
© 2023 Mathematica Scandinavica. All rights reserved.

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