BANACH-STEINHAUS TYPE THEOREMS FOR STATISTICAL AND I-CONVERGENCE WITH APPLICATIONS TO MATRIX MAPS

作者：Kolk Enno^*

来源：Rocky Mountain Journal of Mathematics, 2010, 40(1): 279-289.

DOI：10.1216/RMJ-2010-40-1-279

Let (A(n)) be a sequence of bounded linear operators from a Banach space X into a Banach space Y. It is proved that if X has a countable fundamental set Phi and the ideal I of subsets of N has property (APO), then (A(n)x) is boundedly I-convergent for each x is an element of X if and only if sup(n) parallel to A(n)parallel to < infinity and (A(n)phi) is I-convergent for any phi is an element of Phi. This result is applied to characterize some sequence-to-sequence transformations defined by infinite matrices of bounded linear operators.

• 出版日期2010