On the complete bounds of Lp -Schur multipliers

Journal article (2019)

Authors

M.P.T. Caspers Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2019 M.P.T. Caspers, Guillermo Wildschut
DOI: https://doi.org/10.1007/s00013-019-01316-7
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Published Date

2019

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We study the class Mp of Schur multipliers on the Schatten-von Neumann class Sp with 1 ≤ p≤ ∞ as well as the class of completely bounded Schur multipliers Mpcb. We first show that for 2 ≤ p< q≤ ∞ there exists m∈Mpcb with m∉ Mq, so in particular the following inclusions that follow from interpolation are strict: Mq⊊ Mp and Mqcb⊊Mpcb. In the remainder of the paper we collect computational evidence that for p≠ 1 , 2 , ∞ we have Mp=Mpcb, moreover with equality of bounds and complete bounds. This would suggest that a conjecture raised by Pisier (Astérisque 247:vi+131, 1998) is false.