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Search: All articles in the CMB digital archive with keyword commutant

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1. CMB 2014 (vol 58 pp. 91)

Hasegawa, Kei
 Essential Commutants of Semicrossed Products Let $\alpha\colon G\curvearrowright M$ 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. Keywords:essential commutant, semicrossed productCategories:47L65, 47A55

2. CMB 2000 (vol 43 pp. 21)

Barnes, Bruce A.
 The Commutant of an Abstract Backward Shift A bounded linear operator $T$ on a Banach space $X$ is an abstract backward shift if the nullspace of $T$ is one dimensional, and the union of the null spaces of $T^k$ for all $k \geq 1$ is dense in $X$. In this paper it is shown that the commutant of an abstract backward shift is an integral domain. This result is used to derive properties of operators in the commutant. Keywords:backward shift, commutantCategory:47A99