On the complete bounds of Lp-Schur multipliers
On the complete bounds of Lp-Schur multipliers
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发表时间：
2019
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通讯作者：
M. Caspers;Guillermo Wildschut
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作者：
M. Caspers;Guillermo Wildschut
研究了Schattenvon Neumann类Sp上1≤p≤∞的Schur乘子的Mp类和完全有界Schur乘子的mbb p类。我们首先证明了对于2≤p < q≤∞，存在m∈Mcb p且m∈Mq，因此特别地，由插值得到的下列包含项是严格的：Mq Mp和Mcb q Mcb p。在本文的剩余部分，我们收集了计算证据，证明对于p = 1,2,∞，我们有Mp = Mcb p，并且具有界和完全界的等式。这将表明Pisier提出的一个猜想（ast<s:1> risque 247:vi+131, 1998）是错误的。数学学科分类。47B10, 47L20, 47A30。
We study the class Mp of Schur multipliers on the Schattenvon Neumann class Sp with 1 ≤ p ≤ ∞ as well as the class of completely bounded Schur multipliers Mcb p . We first show that for 2 ≤ p < q ≤ ∞ there exists m ∈ Mcb p with m ∈ Mq, so in particular the following inclusions that follow from interpolation are strict: Mq Mp and Mcb q Mcb p . In the remainder of the paper we collect computational evidence that for p = 1, 2,∞ we have Mp = Mcb p , moreover with equality of bounds and complete bounds. This would suggest that a conjecture raised by Pisier (Astérisque 247:vi+131, 1998) is false. Mathematics Subject Classification. 47B10, 47L20, 47A30.