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Use of reproducing kernels and Berezin symbols technique in some questions of operator theory
Published/Copyright:
May 1, 2012
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.
Received: 2009-10-15
Revised: 2010-03-16
Published Online: 2012-05-01
Published in Print: 2012-May
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Hardy space;
Bergman space;
reproducing kernel;
Berezin
symbol;
compact operator
Articles in the same Issue
- Masthead
- -variable fractals: dimension results
- Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators
- Phylogenetic analysis and homology
- Rational homotopy type of the moduli of representations with Borel mold
- Transcendence of special values of quasi-modular forms
- Use of reproducing kernels and Berezin symbols technique in some questions of operator theory
- Infinite-dimensional supermanifolds over arbitrary base fields
- Weyl and Zariski chambers on K3 surfaces
- The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences
- Solving algebraic equations in roots of unity
