• 제목/요약/키워드: truncated Toeplitz operator

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TRUNCATED HANKEL OPERATORS AND THEIR MATRICES

  • Lanucha, Bartosz;Michalska, Malgorzata
    • 대한수학회보
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    • 제56권1호
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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.

NEW INEQUALITIES VIA BEREZIN SYMBOLS AND RELATED QUESTIONS

  • Ramiz Tapdigoglu;Najwa Altwaijry;Mubariz Garayev
    • Korean Journal of Mathematics
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    • 제31권1호
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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 kλ 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.