Sequential Evaluation Convergence of Operator Series and Its Application. (25th October 2020) - Liu, Hongli; Liu, Guanqi
Abstract: For a class of classical vector-valued sequence spaces in Banach spaces, this article introduces a class of important subsets, which contain all the fully bounded sets and many non-bounded sets in the sequence spaces. Using this collection class, we obtain a convergence theorem for the assignment of series of operator series, and apply the conclusion to the characterization of infinite matrix transformations. In this article, the usual linear constraints on operators are completely removed, and the results obtained greatly increase the possibility of applications.