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On spectra of Hausdorff operators on $ l\sp{2}\sb{+}$


Author: James A. Deddens
Journal: Proc. Amer. Math. Soc. 72 (1978), 74-76
MSC: Primary 47A10; Secondary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1978-0500207-7
MathSciNet review: 0500207
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Abstract: In this note we compute the spectra of all Hausdorff operators on $ l_ + ^2$. We also compute the norm and point spectra of the adjoint. Our technique uses standard operator theory and analytic function theory.


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

  • [1] J. A. Deddens, Analytic Toeplitz and composition operators, Canad. J. Math. 24 (1972), 859-865. MR 0310691 (46:9789)
  • [2] P. R. Halmos, Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)
  • [3] F. Hausdorff, Summationsmethoden und momentfolgen. I, Math Z. 9 (1921), 74-109. MR 1544453
  • [4] W. A. Hurwitz and L. L. Silverman, On the consistency and equivalence of certain definitions of summability, Trans. Amer. Math. Soc. 18 (1917), 1-20. MR 1501058
  • [5] T. L. Kriete and D. Trutt, The Cesàro operator in $ {l^2}$ is subnormal, Amer. J. Math. 93 (1971), 215-225. MR 0281025 (43:6744)
  • [6] B. E. Rhoades, Spectra of some Hausdorff operators, Acta Sci. Math. (Szeged) 32 (1971), 91-100. MR 0305108 (46:4238)
  • [7] A. L. Shields and L. J. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. MR 0287352 (44:4558)
  • [8] T. Yoshino, Subnormal operator with a cyclic vector, Tôhoku Math. J. 21 (1969), 49-55. MR 0246145 (39:7450)
  • [9] G. Leibowitz, Discrete Hausdorff transformations, Proc. Amer. Math. Soc. 38 (1973), 541-544. MR 0315508 (47:4057)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0500207-7
Keywords: Hausdorff matrices, Cesàro operator, spectrum, norm
Article copyright: © Copyright 1978 American Mathematical Society

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