Abstract
We give in terms of Berezin
symbols some characterizations for the operators belonging to the
Schatten–von Neumann classes
,
,
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.