Connections between Deddens algebras and extended eigenvectors

A complex number λ is called an extended eigenvalue of the shift operator S , Sf = zf , on the disc algebra if there exists a nonzero operator satisfying the equation AS = λSA . We describe the set of all extended eigenvectors of S in terms of multiplication operators and composition operators. It i...

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Bibliographic Details
Published in:Mathematical Notes 2011-08, Vol.90 (1-2), p.37-40
Main Author: Gürdal, M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:A complex number λ is called an extended eigenvalue of the shift operator S , Sf = zf , on the disc algebra if there exists a nonzero operator satisfying the equation AS = λSA . We describe the set of all extended eigenvectors of S in terms of multiplication operators and composition operators. It is shown that there are connections between the Deddens algebra associated with S and the extended eigenvectors of S .
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434611070054