Description of invariant subspaces in terms of Berezin symbols

SALTAN S.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.6, pp.2926-2934, 2018 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1801-6
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2926-2934

Abstract

We consider the stretching operator (T(w)f)(z) = f (wz) and the multiple shift operator S-n f = z(n) f on the Hardy spaces H-P(D) (1 <= p < +infinity). We describe in terms of so-called Berezin symbols their lattice of invariant subspaces. We also define a new class of operators on the reproducing kernel Hilbert space H(Omega), which in a particular case contains all compact operators, and discuss in terms of Berezin symbols their invariant subspaces.