By using Hardy-Hilbert's inequality, some power inequalities for the Berezin number of a selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.
We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.
Abstract. We investigate some problems related with Berezin symbols of operators on Hardy and Bergman spaces and their applications in summability theory and in solution of Beurling problem. We also study boundedness and invertibility of some Toeplitz products on the Hardy and Bergman spaces.Mathematics subject classification (2010): Primary 47B35.
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