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Search: MSC category 47A55 ( Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] )

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1. CMB Online first

Dimassi, Mouez
 Semi-classical asymptotics for SchrÃ¶dinger operator with oscillating decaying potential We study the distribution of the discrete spectrum of the SchrÃ¶dinger operator perturbed by a fast oscillating decaying potential depending on a small parameter $h$. Keywords:periodic SchrÃ¶dinger operator, semi-classical asymptotics, effective Hamiltonian, asymptotic expansion, spectral shift functionCategories:81Q10, 35P20, 47A55, 47N50, 81Q15

2. 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
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