Hankel operators with discontinuous symbol
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- by Stephen Power PDF
- Proc. Amer. Math. Soc. 65 (1977), 77-79 Request permission
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
- F. F. Bonsall and S. C. Power, A proof of Hartman’s theorem on compact Hankel operators, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 447–450. MR 383133, DOI 10.1017/S0305004100051914
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
- Philip Hartman, On completely continuous Hankel matrices, Proc. Amer. Math. Soc. 9 (1958), 862–866. MR 108684, DOI 10.1090/S0002-9939-1958-0108684-8 S. C. Power, Intertwining operators, Ph.D. Thesis, Univ. of Edinburgh, 1976.
- Harold Widom, Hankel matrices, Trans. Amer. Math. Soc. 121 (1966), 1–35. MR 187099, DOI 10.1090/S0002-9947-1966-0187099-X
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 77-79
- MSC: Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1977-0512867-4
- MathSciNet review: 0512867