Reflexivity of isometries

Wing-Suet Li; John McCarthy

Studia Mathematica (1997)

  • Volume: 124, Issue: 2, page 101-105
  • ISSN: 0039-3223

Abstract

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

How to cite

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Li, Wing-Suet, and McCarthy, John. "Reflexivity of isometries." Studia Mathematica 124.2 (1997): 101-105. <http://eudml.org/doc/216400>.

@article{Li1997,
abstract = {We prove that any set of commuting isometries on a separable Hilbert space is reflexive.},
author = {Li, Wing-Suet, McCarthy, John},
journal = {Studia Mathematica},
keywords = {reflexivity; set of commuting isometries; separable Hilbert space},
language = {eng},
number = {2},
pages = {101-105},
title = {Reflexivity of isometries},
url = {http://eudml.org/doc/216400},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Li, Wing-Suet
AU - McCarthy, John
TI - Reflexivity of isometries
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 2
SP - 101
EP - 105
AB - We prove that any set of commuting isometries on a separable Hilbert space is reflexive.
LA - eng
KW - reflexivity; set of commuting isometries; separable Hilbert space
UR - http://eudml.org/doc/216400
ER -

References

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  1. [1] H. Bercovici, A factorization theorem with applications to invariant subspaces and the reflexivity of isometries, preprint. Zbl0833.47003
  2. [2] H. Bercovici and W. S. Li, Reflexivity of certain pairs of commuting isometries, preprint. Zbl0872.47002
  3. [3] J. B. Conway, The Theory of Subnormal Operators, Amer. Math. Soc., Providence, 1991. Zbl0743.47012
  4. [4] J. A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971), 509-512. Zbl0213.14304
  5. [5] D. Hadwin and E. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 3-23. Zbl0483.47023
  6. [6] K. Horák and V. Müller, On commuting isometries, Czechoslovak Math. J. 43 (118) (1993), 373-382. Zbl0811.47040
  7. [7] J. E. McCarthy, Reflexivity of subnormal operators, Pacific J. Math. 161 (1993), 359-370. Zbl0792.47027
  8. [8] M. Ptak, Reflexivity of pairs of isometries, Studia Math. 83 (1986), 47-55. 
  9. [9] M. Ptak, Erratum to the paper "Reflexivity of pairs of isometries", ibid. 103 (1992), 221-223. 
  10. [10] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1996), 511-517. Zbl0171.33703

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