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Interwinings of isometric semigroups and Wold type decompositions. (English) Zbl 0596.47027

Summary: In the first part it is shown that different Wold type decompositions of two isometric semigroups are preserved in some sense, if they are doubly intertwined. In the last part the case of two generated isometric semigroups is considered and with its aid we illustrate the existence of some particular Wold type decompositions.

MSC:

47D03 Groups and semigroups of linear operators
47A15 Invariant subspaces of linear operators
47A20 Dilations, extensions, compressions of linear operators
47B47 Commutators, derivations, elementary operators, etc.