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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Isometric dilations for infinite sequences of noncommuting operators

Author: Gelu Popescu
Journal: Trans. Amer. Math. Soc. 316 (1989), 523-536
MSC: Primary 47A20; Secondary 47A45
MathSciNet review: 972704
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Abstract: This paper develops a dilation theory for $ \{ {T_n}\} _{n = 1}^\infty $ an infinite sequence of noncommuting operators on a Hilbert space, when the matrix $ [{T_1},{T_2}, \ldots ]$ is a contraction. A Wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for $ \{ {T_n}\} _{n = 1}^\infty $ are obtained. Some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given. This results are used to extend the Sz.-Nagy-Foiaş lifting theorem to this noncommutative setting.

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Keywords: Isometric dilation, Wold decomposition, lifting theorem
Article copyright: © Copyright 1989 American Mathematical Society