Essential commutants of semicrossed products
Autor: | Hasegawa, Kei |
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Rok vydání: | 2014 |
Předmět: | |
Zdroj: | Can. Math. Bull. 58 (2015) 91-104 |
Druh dokumentu: | Working Paper |
DOI: | 10.4153/CMB-2014-057-x |
Popis: | Let $\alpha:G \curvearrowright M$ be a spatial action of countable abelian group on a "spatial" von Neumann algebra $M$ and $S$ be its unital subsemigroup with $G=S^{-1}S$. We explicitly compute the essential commutant and the essential fixed-points, modulo the Schatten $p$-class or the compact operators, of the w$^*$-semicrossed product of $M$ by $S$ when $M'$ contains no non-zero compact operators. We also prove a weaker result when $M$ is a von Neumann algebra on a finite dimensional Hilbert space and $(G,S)=(\mathbb{Z},\mathbb{Z}_{+})$, which extends a famous result due to Davidson (1977) for the classical analytic Toeplitz operators. Comment: 13 pages |
Databáze: | arXiv |
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