Essential Commutants of Semicrossed Products

Canadian mathematical bulletin

Kei Hasegawa¹ 

[1] Graduate School of Mathematics, Kyushu University, Fukuoka 819-0395, Japan

关键词: essential commutant;    semicrossed product;   

DOI  :  10.4153/CMB-2014-057-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $alphacolon Gcurvearrowright M$ be a spatial action of countableabelian group on a "spatial" von Neumann algebra $M$ and $S$ be itsunital subsemigroup with $G=S^{-1}S$. We explicitly compute theessential commutant and the essential fixed-points, modulo theSchatten $p$-class or the compact operators, of the w$^*$-semicrossedproduct of $M$ by $S$ when $M'$ contains no non-zero compactoperators. We also prove a weaker result when $M$ is a von Neumannalgebra on a finite dimensional Hilbert space and$(G,S)=(mathbb{Z},mathbb{Z}_+)$, which extends a famous result dueto Davidson (1977) for the classical analytic Toeplitz operators.

【 授权许可】

Unknown