Description of invariant subspaces in terms of Berezin symbols
TURKISH JOURNAL OF MATHEMATICS, vol.42, no.6, pp.2926-2934, 2018 (SCI-Expanded, Scopus, TRDizin)
- 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 (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.2926-2934
- Süleyman Demirel University Affiliated: Yes
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.