Discrete generalized Cesàro operators
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- by H. C. Rhaly
- Proc. Amer. Math. Soc. 86 (1982), 405-409
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671204-7
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Abstract:
For $\left | \lambda \right | \leqslant 1$, $A_\lambda ^*$ is the operator defined formally on the Hardy space ${H^2}$ by \[ (A_\lambda ^*f)(z) = - {(\lambda - z)^{ - 1}}\int _\lambda ^z {f(s) } ds,\quad \left | z \right | < 1.\] 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
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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