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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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 }$.

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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