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

摘要

We give in terms of Berezin symbols some characterizations for the operators belonging to the Schatten-von Neumann classes σ _p, 0 < p < +~∞, 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.