On a conjecture of Pisier on the analyticity of semigroups

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• 作者：Cédric Arhancet
• 关键词：Noncommutative $$L^p$$ L p ; spaces ; Operator spaces ; Analytic semigroups ; K ; convexity ; Fourier multipliers ; Schur multipliers
• 刊名：Semigroup Forum
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：91
• 期：2
• 页码：450-462
• 全文大小：446 KB
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• 作者单位：Cédric Arhancet (1)
  
  1. Laboratoire de Mathématiques, Université de Franche-Comté, 25030, Besan?on Cedex, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137

文摘

We show that the analyticity of semigroups \((T_t)_{t \geqslant 0}\) of selfadjoint contractive Fourier multipliers on \(L^p\)-spaces of compact abelian groups is preserved by the tensorisation of the identity operator of a Banach space for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. We also give versions of this result for some semigroups of Schur multipliers and Fourier multipliers on noncommutative \(L^p\)-spaces. Finally, we give a precise description of semigroups of Schur multipliers to which the result of this paper can be applied. Keywords Noncommutative \(L^p\)-spaces Operator spaces Analytic semigroups K-convexity Fourier multipliers Schur multipliers