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A Simple Proof of the Fundamental Theorem about Arveson Systems

Research paper by M. Skeide

Indexed on: 08 Jul '06Published on: 08 Jul '06Published in: Mathematics - Operator Algebras



Abstract

With every Eo-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an Eo-semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and allows for a generalization to product systems of Hilbert module (to be published elsewhere).