On the complete bounds of Lp -Schur multipliers

Martijn Caspers*, Guillermo Wildschut

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)189-200
Number of pages12
JournalArchiv der Mathematik
Volume113
Issue number2
DOIs
Publication statusPublished - 2019

Keywords

  • Non-commutative L-spaces
  • Operator spaces
  • Schur multipliers

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