F?lner sequences and finite operators

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• 作者：Fernando Lledó ; ^a ; ^b ; ^{flledo@math.uc3m.es} ; Dmitry V. Yakubovich^c ; ^b ; ^{dmitry.yakubovich@uam.es}
• 关键词：Finite operators ; Essentially normal operators ; Quasinormal operators ; Non-normal operators ; Fø ; lner sequences ; C*-algebras ; Cuntz algebras
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：15 July, 2013
• 年：2013
• 卷：403
• 期：2
• 页码：464-476
• 全文大小：439 K

文摘

This article analyzes F?lner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70s. We prove that each essentially hyponormal operator has a proper F?lner sequence (i.e., an increasing F?lner sequence of projections strongly converging to ). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper F?lner sequence. Moreover, we show that an operator is finite if and only if it has a proper F?lner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no F?lner sequence and give examples of them. For this analysis we introduce the notion of strongly non-F?lner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non finite operators.