Wold decomposition for representations of product systems of C*-correspondences
Operator Algebras
2007-05-23 v2 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.math/0702649,
title = {Wold decomposition for representations of product systems of C*-correspondences},
author = {Adam Skalski and Joachim Zacharias},
journal= {arXiv preprint arXiv:math/0702649},
year = {2007}
}
Comments
21 pages, to appear in the International Journal of Mathematics (v2: typos corrected, Section 5 extended and connections with the earlier work of Paul Muhly and Baruch Solel clarified)