M.Sc Thesis
M.Sc Student Talker Oded Wold Decomposition for Commuting Row Isometries Department of Mathematics Professor Baruch Solel

Abstract

Given a Hilbert space H and an isometry V in B(H), the classical Wold decomposition theorem states that the space H decomposes as H = H1 + H2 such that each Hi, i = 1, 2 reduces V, V|H1 is unitary and V|H2 is a unilateral shift.

There are known generalizations of this theorem for a row isometry, doubly commuting pair of isometries, for isometric covariant representations of a C*-correspondences and for a doubly commuting isometric representations of a product system of C*-correspondences.

In this study, we prove the existence of a Wold decomposition for pairs of a doubly commuting row isometries. We present models which classify such pairs and use these models to construct a unitary extension of the doubly commuting row isometries.