Korean Journal of Mathematics

  • 제31권1호
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  • Pages.109-120
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  • 2023
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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NEW INEQUALITIES VIA BEREZIN SYMBOLS AND RELATED QUESTIONS

  • Ramiz Tapdigoglu (Department of Mathematics, Azerbaijan State University of Economics (UNEC) and Khazar University) ;
  • Najwa Altwaijry (Department of Mathematics, College of Science, King Saud University) ;
  • Mubariz Garayev (Department of Mathematics, College of Science, King Saud University)
  • 투고 : 2021.09.22
  • 심사 : 2023.01.09
  • 발행 : 2023.03.30
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

The first and second authors extend their appreciation to the Distinguished Scientist Fellowship Program at King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project number (RSP2023R187). Also, the third author thanks to Deanship of Scientific Research, College of Science Research Center, King Saud University for supporting this work.

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