Isometric dilations for infinite sequences of noncommuting operators

Transactions of the American Mathematical Society - Tập 316 Số 2 - Trang 523-536
Gelu Popescu1
1INCREST

Tóm tắt

This paper develops a dilation theory for { T n } n = 1 ∞ \{ {T_n}\} _{n = 1}^\infty an infinite sequence of noncommuting operators on a Hilbert space, when the matrix [ T 1 , T 2 , … ] [{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 ∞ \{ {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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Tài liệu tham khảo

Douglas, R. G., 1968, Lifting commuting operators, Michigan Math. J., 15, 385, 10.1307/mmj/1029000093

Foiaş, Ciprian, 1963, A remark on the universal model for contractions of G. C. Rota, Com. Acad. R. P. Rom\^{\i}ne, 13, 349

Frazho, Arthur E., 1982, Models for noncommuting operators, J. Functional Analysis, 48, 1, 10.1016/0022-1236(82)90057-X

Frazho, Arthur E., 1984, Complements to models for noncommuting operators, J. Funct. Anal., 59, 445, 10.1016/0022-1236(84)90059-4

Popescu, Gelu, 1989, Models for infinite sequences of noncommuting operators, Acta Sci. Math. (Szeged), 53, 355

Schäffer, J. J., 1955, On unitary dilations of contractions, Proc. Amer. Math. Soc., 6, 322, 10.2307/2032368

Sz.-Nagy, Béla, 1968, Dilatation des commutants d’opérateurs, C. R. Acad. Sci. Paris S\'{e}r. A-B, 266, A493--A495

\bysame, Harmonic analysis on operators on Hilbert space, North-Holland, Amsterdam, 1970.

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Transactions of the American Mathematical Society

Tập 316 Số 2

523-536

Thông tin tác giả