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A Wold-type decomposition for commuting isometric pairs

Authors:	Dan Popovici

Institution:	Department of Mathematics, University of the West Timisoara, RO-300223 Timisoara, Bd. Vasile Pârvan nr. 4, Romania

Abstract:	We obtain a Wold-type decomposition theorem for an arbitrary pair of commuting isometries on a Hilbert space. More precisely, can be uniquely decomposed into the orthogonal sum between a bi-unitary, a shift-unitary, a unitary-shift and a weak bi-shift part, that is, a part that can be characterized by the condition that $S_1S_2, S_1\vert _{\bigcap_{n\ge 0}\ker S_2^S_1^n}$ and $S_2\vert _{\bigcap_{n\ge 0}\ker S_1^S_2^n}$ are shifts. Moreover, contains bi-shift and modified bi-shift maximal parts.

Keywords:	Wold-type decomposition (dual) bi-isometry (weak modified) bi-shift unitary extension

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