On Certain Vector Valued Multiplier Spaces and Series of Operators

Abstract

By L (X, Y), we denote the space of all continuous linear operators between the normed spaces X and Y. In [15], Swartz introduced the (bounded) multiplier space for the series Sigma T-j as: M-infinity (Sigma T-j) = {x = (x(j)) is an element of l(infinity) (X)vertical bar Sigma(j)T(j)x(j) converges}, where (T-j) subset of L (X, Y). Recently in [6], Altay and Kama de fined the vector valued multiplier space M-C(infinity) (T) of Cesaro convergence by using Cesaro summability method as follow: M-C(infinity) (T) = {x = (x(k)) is an element of l(infinity) (X)vertical bar Sigma(k)T(j)x(j) converges}, In this paper, we introduce the vector valued multiplier spaces S-Lambda (T) and S-w Lambda (T) by means of Lambda- convergence and a sequence of continuous linear operators and study a series of some properties of these spaces.