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Subnormality and quasinormality of Toeplitz operators


Authors: Takashi Itô and Tin Kin Wong
Journal: Proc. Amer. Math. Soc. 34 (1972), 157-164
MSC: Primary 47B35
DOI: https://doi.org/10.1090/S0002-9939-1972-0303334-7
MathSciNet review: 0303334
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Abstract: Halmos asks whether every subnormal Toeplitz operator on $ {H^2}$ is either analytic or normal. It is shown that for a certain class of Toeplitz operators, the subnormality implies either analyticity or normality.


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  • [1] A. Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723-728. MR 15, 538. MR 0059483 (15:538c)
  • [2] A. Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89-102. MR 28 #3350; errata MR 30, 1205. MR 0160136 (28:3350)
  • [3] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 42 #5066. MR 0270173 (42:5066)
  • [4] -, A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967. MR 34 #8178. MR 0208368 (34:8178)
  • [5] -, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102-112. MR 27 #2868. MR 0152896 (27:2868)
  • [6] H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 30 #1409. MR 0171178 (30:1409)
  • [7] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1962. MR 24 #A2844. MR 0133008 (24:A2844)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0303334-7
Keywords: Toeplitz operator, subnormal operator, quasinormal operator, hyponormal operator
Article copyright: © Copyright 1972 American Mathematical Society

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