Folner sequences and finite operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Lledo, Fernando^1,2  Yakubovich, Dmitry V.^2,3 

[1] Univ Carlos III Madrid, Dept Math, E-28911 Leganes, Madrid, Spain

[2] Inst Ciencias Matemat CSIC UAM UC3M UCM, Madrid, Spain

[3] Univ Autonoma Madrid, Dept Matemat, Canto Blanco 28049, Madrid, Spain

关键词: Finite operators;    Essentially normal operators;    Quasinormal operators;    Non-normal operators;    Folner sequences;    C*-algebras;    Cuntz algebras;   

DOI  :  10.1016/j.jmaa.2013.02.037

来源: Elsevier

【 摘 要 】

This article analyzes Folner 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 Folner sequence (i.e., an increasing Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free