(e)-Convergence for double sequences

Ulaş Yamancı

doi:10.26637/mjm904/005

Abstract

We define the notion of (e)-summability of double sequences and series of complex numbers. We also obtain a criteria for this summability method with regards to Berezin symbols of an diagonal operator, and show regularity of (e)-summability method for double sequences.

Highlights

A reproducing kernel Hilbert space H = H(Ω) on some set Ω is a Hilbert space of functions on Ω such that for every λ ∈ Ω the linear functional f → f (λ) is bounded on H
We know that provided thatj∈J is an orthonormal basis for the RKHS H
We obtain a criteria for this summability method with regards to Berezin symbols of an diagonal operator, and show regularity of (e)-summability method for double sequences

Summary

Introduction

Let A be a bounded operator on reproducing kernel Hilbert spaces. A(λ) :=< Akλ, kλ >, λ ∈ Ω, is called the Berezin symbol, which is a bounded function by the norm of the operator (see [2]). On the reproducing kernel Hilbert spaces, A1 (λ) = A2 (λ) for all λ implies A1 = A2, that is, the Berezin symbol uniquely determines the operator.

Results

Conclusion