H[∞]functional calculus and square functions on noncommutative L[p]-spaces

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
M. Junge, C. Merdy, Quanhua Xu
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引用次数: 94

Abstract

— We investigate sectorial operators and semigroups acting on noncommutative L-spaces. We introduce new square functions in this context and study their connection with H∞ functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative L-spaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative L-spaces. We mainly focus on noncommutative diffusion semigroups, that is, semigroups (Tt)t≥0 of normal selfadjoint operators on a semifinite von Neumann algebra (M, τ) such that Tt : Lp(M) → Lp(M) is a contraction for any p ≥ 1 and any t ≥ 0. We discuss several examples of such semigroups for which we establish bounded H∞ functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck semigroups acting on the q-deformed von Neumann algebras of Bozejko-Speicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group. c © Astérisque 305, SMF 2006
非交换L[p]-空间上的H[∞]泛函微积分与平方函数
研究了作用于非交换l空间上的扇区算子和半群。在此背景下,我们引入了新的平方函数,并研究了它们与H∞泛函微积分的联系,推广了Cowling、Doust、McIntoch和Yagi关于可交换l空间的一些著名工作。这需要Rademacher扇形的自然变异体和非交换l空间的材料结构的使用。我们主要研究半有限von Neumann代数(M, τ)上的正规自伴随算子的非交换扩散半群(Tt)t≥0,使得Tt: Lp(M)→Lp(M)是任意p≥1和任意t≥0的收缩。我们讨论了这类半群的几个例子,并建立了有界H∞泛函演算和平方函数估计。这包括由某些hamilton或Schur乘子生成的半群,作用于bozejco - speicher的q-变形冯·诺伊曼代数上的q-Ornstein-Uhlenbeck半群,以及作用于自由群的群冯·诺伊曼代数上的非交换泊松半群。c©ast risque 305, SMF 2006
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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