Illinois Journal of Mathematics

Hausdorff matrices and composition operators

Petros Galanopoulos and Aristomenis G. Siskakis

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We consider Hausdorff matrices as operators on Hardy spaces of analytic functions. When the generating sequence of the matrix is the moment sequence of a measure $\mu$, we find conditions on $\mu$ such that the matrix represents a bounded operator. The results unify and extend some known special cases of operators on Hardy spaces such as the Cesàro and generalized Cesàro operators.

Article information

Illinois J. Math., Volume 45, Number 3 (2001), 757-773.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 47B33: Composition operators
Secondary: 30D55 40G05: Cesàro, Euler, Nörlund and Hausdorff methods 46E15: Banach spaces of continuous, differentiable or analytic functions 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]


Galanopoulos, Petros; Siskakis, Aristomenis G. Hausdorff matrices and composition operators. Illinois J. Math. 45 (2001), no. 3, 757--773. doi:10.1215/ijm/1258138149.

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