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Discrete generalized Cesàro operators


Author: H. C. Rhaly
Journal: Proc. Amer. Math. Soc. 86 (1982), 405-409
MSC: Primary 47B99
DOI: https://doi.org/10.1090/S0002-9939-1982-0671204-7
MathSciNet review: 671204
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Abstract: For $ \left\vert \lambda \right\vert \leqslant 1$, $ A_\lambda ^*$ is the operator defined formally on the Hardy space $ {H^2}$ by

$\displaystyle (A_\lambda ^*f)(z) = - {(\lambda - z)^{ - 1}}\int_\lambda ^z {f(s)\,} ds,\quad \left\vert z \right\vert < 1.$

If $ \lambda = 1$, then the usual identification of $ {H^2}$ with $ {l^2}$ takes $ {A_1}$ onto the discrete Cesàro operator. Here we answer questions about boundedness, spectra, unitary equivalence, compactness, and subnormality for the operators $ {A_\lambda }$.

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

  • [1] A. Brown, P. R. Halmos and A. L. Shields, Cesàro operators, Acta Sci. Math. (Szeged) 26 (1965), 125-137. MR 0187085 (32:4539)
  • [2] P. L. Duren, Theory of $ {H^p}$ spaces, Academic Press, New York, 1970. MR 0268655 (42:3552)
  • [3] P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)
  • [4] 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)
  • [5] T. L. Kriete, Generalized Cesàro operators, unpublished.
  • [6] W. Rudin, Functional analysis, McGraw-Hill, New York, 1973. MR 0365062 (51:1315)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0671204-7
Keywords: Cesàro operator, spectrum, compact operator, subnormal operator
Article copyright: © Copyright 1982 American Mathematical Society

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