ON BOREL CONVERGENCE OF DOUBLE SEQUENCES

In this paper, we introduce the concept of (Ber)-convergence of bounded double sequences in the Fock space F (C-2). We show that every (Ber)-convergent double sequence is Borel convergent. Namely, we prove the following theorem by using the Berezin symbol method: If the {x(ij)}(i,j=0)(infinity) is regularly convergent to x, then