Connections between Deddens algebras and extended eigenvectors

Gurdal M.

MATHEMATICAL NOTES, cilt.90, ss.37-40, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 90
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1134/s0001434611070054
  • Dergi Adı: MATHEMATICAL NOTES
  • Sayfa Sayıları: ss.37-40

Özet

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.