Wold decomposition for representations of product systems of C*-correspondences

Details Wold decomposition for representations of product systems of C*-correspondences Wold decomposition for representations of product systems of C*-correspondences

2007-02-22

arxiv.org/abs/math/0702649v2

Mathematics

Operator Algebras

21 pages, to appear in the International Journal of Mathematics (v2: typos corrected, Section 5 extended and connections with

Scientific paper

Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C*-correspondences over N^k, generalising the classical result for a doubly commuting pair of isometries due to M.Slocinski. Certain decompositions are also obtained for the general, not necessarily doubly commuting, case and several corollaries and examples are provided. Possibilities of extending isometric representations to fully coisometric ones are discussed.

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