OPERATOR INEQUALITIES IN REPRODUCING KERNEL HILBERT SPACES


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YAMANCI U.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.71, no.1, pp.204-211, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.31801/cfsuasmas.926981
  • Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Journal Indexes: Emerging Sources Citation Index, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.204-211
  • Keywords: Mulholland type inequality, Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol, NUMERICAL RADIUS INEQUALITIES, BEREZIN NUMBER INEQUALITIES, NONCOMMUTATIVE HARDY

Abstract

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number ber(A) for some self-adjoint operators A on H(Omega). Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that (ber(A))(n) <= C(1)ber(A(n)) for any positive operator A on H(Omega).