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Schur multipliers of Schatten–von Neumann classes
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.jfa.2020.108683
A.B. Aleksandrov , V.V. Peller

Abstract We study in this paper properties of Schur multipliers of Schatten von Neumann classes S p . We prove that for p ≤ 1 , Schur multipliers of S p are necessarily completely bounded. We also introduce for p ≤ 1 a scale W p of tensor products of l ∞ and prove that matrices in W p are Schur multipliers of S p . We compare this sufficient condition with the sufficient condition of membership in the p-tensor product of l ∞ spaces.

中文翻译:

Schatten-von Neumann 类的 Schur 乘数

摘要 本文研究了Schatten von Neumann 类Sp 的Schur 乘子的性质。我们证明当 p ≤ 1 时,Sp 的 Schur 乘子必然是完全有界的。我们还为 p ≤ 1 引入了 l ∞ 张量积的尺度 W p 并证明了 W p 中的矩阵是 Sp 的 Schur 乘子。我们将这个充分条件与 l ∞ 空间的 p-张量积的成员资格充分条件进行比较。
更新日期:2020-11-01
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