Geodesic
Connections between Deddens Algebras and Extended Eigenvectors
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 40-44

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A complex number $\lambda$ is called an extended eigenvalue of the shift operator $S$, $Sf=zf$, on the disc algebra $C_{A}(\mathbb{D})$ if there exists a nonzero operator $A\colon C_{A}(\mathbb{D}) \to C_{A}(\mathbb{D})$ satisfying the equation $AS=\lambda S\mspace{-3mu}A$. 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 $S$.
Keywords: disc algebra, multiplication operator, extended eigenvalue, extended eigenvector, shift operator, Banach algebra.
Mots-clés : Deddens algebra 
@article{MZM_2011_90_1_a4,
     author = {M. Gurdal},
     title = {Connections between {Deddens} {Algebras} and {Extended} {Eigenvectors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {40--44},
     publisher = {mathdoc},
     volume = {90},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a4/}
}
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M. Gurdal. Connections between Deddens Algebras and Extended Eigenvectors. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 40-44. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a4/