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

Skalski, Adam G. and Zacharias, Joachim (2007) Wold decomposition for isometric representations of product systems of C*-correspondences. International Journal of Mathematics. ISSN 1793-6519

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.