Note on the joint spectrum of the Wiener-Hopf operators
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- by Jan Janas PDF
- Proc. Amer. Math. Soc. 50 (1975), 303-308 Request permission
Abstract:
J. Bunce has given [2] the definition of a joint approximate point spectrum of $p$-tuples of commuting operators in a complex Hilbert space. A. T. Dash after presentation of another type of a joint spectrum, has found this joint spectrum for $p$-tuples of analytic Toeplitz operators [4]. In this paper we will find a joint approximate point spectrum of $p$-tuples of noncommuting selfadjoint Wiener-Hopf operators and prove an inclusion for a joint spectrum of analytic matrix Toeplitz operators.References
- F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, vol. 2, Cambridge University Press, London-New York, 1971. MR 0288583
- John Bunce, The joint spectrum of commuting nonnormal operators, Proc. Amer. Math. Soc. 29 (1971), 499–505. MR 283602, DOI 10.1090/S0002-9939-1971-0283602-7
- L. A. Coburn and R. G. Douglas, $C^{\ast }$-algebras of operators on a half-space. I, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 59–67. MR 358417
- A. T. Dash, Joint spectra, Studia Math. 45 (1973), 225–237. MR 336381, DOI 10.4064/sm-45-3-225-237
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
- Paul A. Fuhrmann, On the corona theorem and its application to spectral problems in Hilbert space, Trans. Amer. Math. Soc. 132 (1968), 55–66. MR 222701, DOI 10.1090/S0002-9947-1968-0222701-7
- E. M. Klein, More algebraic properties of Toeplitz operators, Math. Ann. 202 (1973), 203–207. MR 333812, DOI 10.1007/BF01361718
- H. R. Pousson, Systems of Toeplitz operators on $H^{2}$, Proc. Amer. Math. Soc. 19 (1968), 603–608. MR 225188, DOI 10.1090/S0002-9939-1968-0225188-9
- Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, DOI 10.1016/0022-1236(70)90055-8
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 303-308
- MSC: Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374977-2
- MathSciNet review: 0374977