• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.187-200
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• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.