The structure of an isometric tuple

Abstract

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\dot{.}.V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the classical Lebesgue-von Neumann-Wold decomposition of an isometry into the direct sum of a unilateral shift, an absolutely continuous unitary and a singular unitary. We show that, as in the classical case, this decomposition determines the weakly closed algebra and the von Neumann algebra generated by the tuple.

30 pages; significant changes

References in corpus (2)

• Factoring in Non-commutative Analytic Toeplitz Algebras
• Isometric dilations of non-commuting finite rank $n$-tuples

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