M.Sc Thesis | |

M.Sc Student | Talker Oded |
---|---|

Subject | Wold Decomposition for Commuting Row Isometries |

Department | Department of Mathematics |

Supervisor | PROFESSOR EMERITUS Baruch Solel |

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 = H_{1} +
H_{2} such that each H_{i}, i = 1, 2 reduces V, V|H_{1}
is unitary and V|H_{2} 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.