Use of reproducing kernels and Berezin symbols technique in some questions of operator theory

Karaev M. T.

FORUM MATHEMATICUM, vol.24, no.3, pp.553-564, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.1515/form.2011.073
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.553-564


We give in terms of Berezin symbols some characterizations for the operators belonging to the Schatten-von Neumann classes sigma(p), 0 < p < +infinity, which were motivated by the questions posed by Nordgren and Rosenthal [7]. Some other problems related with the multiplicative equality for Berezin symbols are also discussed. We also prove in terms of Berezin symbols a Gohberg-Krein type theorem on the weak limit of compact operators.