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ArticleOriginal scientific text
Title
Reflexivity of isometries
Authors 1, 2
Affiliations
- Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.
- Washington University, St. Louis, Missouri 63130, U.S.A.
Abstract
We prove that any set of commuting isometries on a separable Hilbert space is reflexive.
Bibliography
- H. Bercovici, A factorization theorem with applications to invariant subspaces and the reflexivity of isometries, preprint.
- H. Bercovici and W. S. Li, Reflexivity of certain pairs of commuting isometries, preprint.
- J. B. Conway, The Theory of Subnormal Operators, Amer. Math. Soc., Providence, 1991.
- J. A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971), 509-512.
- D. Hadwin and E. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 3-23.
- K. Horák and V. Müller, On commuting isometries, Czechoslovak Math. J. 43 (118) (1993), 373-382.
- J. E. McCarthy, Reflexivity of subnormal operators, Pacific J. Math. 161 (1993), 359-370.
- M. Ptak, Reflexivity of pairs of isometries, Studia Math. 83 (1986), 47-55.
- M. Ptak, Erratum to the paper "Reflexivity of pairs of isometries", ibid. 103 (1992), 221-223.
- D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1996), 511-517.