Dynamical entropy in Banach spaces

• 成果类型: Article
• 署名作者: Kerr, D; Li, HF
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of Tokyo; University of Toronto
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0457-9
• 发表日期: 2005
• 页码: 649-686
• 关键词: C-ASTERISK-ALGEBRAS; topological-entropy; approximation entropies; orbit equivalence; crossed-products; zero; systems; rank

摘要

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometrically and topologically. This leads to various applications; for example, we obtain a geometric description of the topological Pinsker factor and show that a C*-algebra is type I if and only if every multiplier inner *-automorphism has zero CA entropy. We also examine the behaviour of CA entropy under various product constructions and determine its value in many examples, including isometric automorphisms of l(p) for 1 <= p <= infinity and noncommutative tensor product shifts.