Reflexivity of isometries

• Autorzy: Wing-Suet Li , John E. McCarthy
• Języki publikacji: EN

Abstrakty

EN

We prove that any set of commuting isometries on a separable Hilbert space is reflexive.

Kategorie tematyczne

• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 2
• Strony: 101-105

Daty

wydano

1997

otrzymano

1994-08-11

poprawiono

1995-10-31

poprawiono

1996-11-14

Twórcy

autor

Wing-Suet Li

• Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.

autor

John E. McCarthy

• Washington University, St. Louis, Missouri 63130, U.S.A.

Bibliografia

• [1] H. Bercovici, A factorization theorem with applications to invariant subspaces and the reflexivity of isometries, preprint.
• [2] H. Bercovici and W. S. Li, Reflexivity of certain pairs of commuting isometries, preprint.
• [3] J. B. Conway, The Theory of Subnormal Operators, Amer. Math. Soc., Providence, 1991.
• [4] J. A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971), 509-512.
• [5] D. Hadwin and E. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 3-23.
• [6] K. Horák and V. Müller, On commuting isometries, Czechoslovak Math. J. 43 (118) (1993), 373-382.
• [7] J. E. McCarthy, Reflexivity of subnormal operators, Pacific J. Math. 161 (1993), 359-370.
• [8] M. Ptak, Reflexivity of pairs of isometries, Studia Math. 83 (1986), 47-55.
• [9] M. Ptak, Erratum to the paper "Reflexivity of pairs of isometries", ibid. 103 (1992), 221-223.
• [10] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1996), 511-517.