The distance formula for the derivation problem

Jaeseong Heo ()
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Jaeseong Heo: Research Institute for Natural Sciences, Hanyang University

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 4, 489-494

Abstract: Abstract In this paper we discuss questions related to the perturbation of von Neumann algebras. We will show that the distance between an arbitrary operator of M and the commutant M′ is the same as the distance from the same operator to the trivial center CI of M where M is a type II-factor in a separable Hilbert space. As a consequence, the derivation implemented by some element x∈M has the same norm as the distance from x to the commutant M′.

Keywords: Type II factor; distance of two C*-algebras; derivation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0148-1

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