Abstract
We look at the point-spectrum of the adjoints of certain composition operators on the Hardy–Hilbert space, for which the composition map has two distinguished fixed points: one inside the unit disk and one on the unit circle. In particular, we show that the point-spectrum of such operators contains a disk centered at the origin, and each eigenvalue in that disk has infinite multiplicity. We also identify for every such operator a subspace of the Hardy–Hilbert space which is invariant for the operator and on which it acts like a weighted shift. Finally, we generalize these results to weighted composition operators.
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This paper is part of a doctoral thesis [9] written under the direction of Professor Carl C. Cowen, Purdue University.
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Neophytou, M. Eigenvalues of Adjoints of Certain Composition Operators and Weighted Composition Operators. Integr. Equ. Oper. Theory 81, 97–111 (2015). https://doi.org/10.1007/s00020-014-2191-4
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DOI: https://doi.org/10.1007/s00020-014-2191-4