Applications of reproducing kernels and Berezin symbols

摘要

Using techniques from the theory of reproducing kernels and Berezin symbols, weinvestigate some problems related to classes of linear operators acting on reproducing kernelHilbert spaces (RKHS's). In particular, we establish new estimates related to the numerical radii andBerezin numbers of some operators on RKHS's. Further, in terms of the distancefunction, we describe invariant subspaces of isometric composition operators on a RKHS H(Ω) of complex-valued, but notnecessarily analytic, functions on a set Ω. Moreover, we consider a modification ofSarason's question about truncated Toeplitz operators. We also discuss related problems.