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On the complete bounds of Lp -Schur multipliers

Journal Article (2019)
Author(s)

Martijn Caspers (TU Delft - Analysis)

Guillermo Wildschut (Student TU Delft)

Research Group
Analysis
Copyright
© 2019 M.P.T. Caspers, Guillermo Wildschut
DOI related publication
https://doi.org/10.1007/s00013-019-01316-7
More Info
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Publication Year
2019
Language
English
Copyright
© 2019 M.P.T. Caspers, Guillermo Wildschut
Research Group
Analysis
Issue number
2
Volume number
113
Pages (from-to)
189-200
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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.