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Hankel operators with discontinuous symbol

Author: Stephen Power
Journal: Proc. Amer. Math. Soc. 65 (1977), 77-79
MSC: Primary 47B35
MathSciNet review: 0512867
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Abstract: Douglas's localisation theory for Toeplitz operators is used to show that there exist certain Hankel operators with discontinuous symbols which do not lie in the $ {C^\ast}$-algebra generated by the Toeplitz operators. As a simple corollary we also see that these operators do not lie in the closed linear span of the positive Hankel operators.

References [Enhancements On Off] (What's this?)

  • [1] F. F. Bonsall and S. C. Power, A proof of Hartman's theorem on compact Hankel operators, Math. Proc. Cambridge Philos. Soc. 78 (1975), 447-450. MR 0383133 (52:4014)
  • [2] R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1973. MR 0361893 (50:14335)
  • [3] P. Hartman, On completely continuous Hankel matrices, Proc. Amer. Math. Soc. 9 (1958), 862-866. MR 0108684 (21:7399)
  • [4] S. C. Power, Intertwining operators, Ph.D. Thesis, Univ. of Edinburgh, 1976.
  • [5] H. Widom, Hankel matrices, Trans. Amer. Math. Soc. 121 (1966), 1-35. MR 0187099 (32:4553)

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Keywords: Hankel operator, discontinuous symbol, Toeplitz operator, $ {C^\ast}$-algebra, positive Hankel operator
Article copyright: © Copyright 1977 American Mathematical Society

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