On some problems for operators on the reproducing kernel Hilbert space. Issue 11 (18th August 2021)

• Record Type: Journal Article
• Authors: Garayev, M. T.; Guediri, H.; Gürdal, M.; Alsahli, G. M.
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 11(2021)
• Page Start: 2059
• Page End: 2077
• Publication Date: 2021-08-18
• Subjects: Reproducing kernel -- Berezin symbol -- Hardy space -- weighted composition operator -- invariant subspace -- Berezin number; Primary 47B35; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1659220
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: In this study, some problems of operator theory on the reproducing kernel Hilbert space by using the Berezin symbols method are investigated. Namely, invariant subspaces of weighted composition operators on H 2 are studied. Moreover, some new inequalities for the Berezin number of operators are proved. In particular, new reverse inequalities for the Berezin numbers b e r A 2 and b e r A of operators A 2 = A ∗ A and A on the reproducing kernel Hilbert space are given. Also, reverse inequalities for the Berezin number of two operators are proved. Under some conditions we prove the power inequality 1 b e r A n ≤ b e r A n which is related to a well known analogue estimate of Halmos for the numerical radius.