Connections between Deddens algebras and extended eigenvectors

Gurdal M.

MATHEMATICAL NOTES, vol.90, pp.37-40, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 90
  • Publication Date: 2011
  • Doi Number: 10.1134/s0001434611070054
  • Title of Journal : MATHEMATICAL NOTES
  • Page Numbers: pp.37-40

Abstract

A complex number. is called an extended eigenvalue of the shift operator S, Sf = zf, on the disc algebra C(A)(D) if there exists a nonzero operator A: C(A)(D) -> C(A)(D) satisfying the equation AS = lambda SA. 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.