On the weak limit of compact operators on the reproducing kernel Hilbert space and related questions

Abstract

By applying the so-called Berezin symbols method we prove a Gohberg- Krein type theorem on the weak limit of compact operators on the non- standard reproducing kernel Hilbert space which essentially improves the similar results of Karaev [5]: We also in terms of reproducing kernels and Berezin symbols investigate the structure of invariant subspaces of compact operators.

Keywords

• compact operator
• reproducing kernel hilbert space
• berezin symbol
• re- producing kernel
• invariant subspace
• primary 47b35
• secondary 47b10