On the complete bounds of L_p-Schur multipliers

2019/02/21 by Martijn Caspers, Caspers, Martijn, Guillermo Wildschut +1
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1902.07949

openalex publication_date 2019/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the class M_p of Schur multipliers on the Schatten-von Neumann class S_p with 1 ≤ p ≤ ∞ as well as the class of completely bounded Schur multipliers M_p^cb. We first show that for 2 ≤ p < q ≤ ∞ there exist m ∈ M_p^cb with m \not ∈ M_q, so in particular the following inclusions that follow from interpolation are strict M_q \subsetneq M_p and M^cb_q \subsetneq M^cb_p. In the remainder of the paper we collect computational evidence that for p\not = 1,2, ∞ we have M_p = M_p^cb, moreover with equality of bounds and complete bounds. This would suggest that a conjecture raised by Pisier is false.

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