Abstract
In this article, a concept of (Ber)-convergence for the multiple sequences (a
k
1
,..., k
N
) of complex numbers is introduced and a Tauberian theorem for such a summability method is proved. We also solve an open question for a bounded single sequence (a
n
)
n≥0
posed by Zorboska in [
10
] in connection with the compactness problem for so-called radial operators on the classical Bergman space
over the unit disc = {z ∈ ℂ: |z| <1}. Our proofs essentially use the Berezin symbols technique of operator theory in the reproducing kernel Hilbert spaces. Namely, we apply the Nordgren-Rosenthal theorem regarding compact operators on a reproducing kernels Hilbert space.