The notation and terminology used here are introduced in the following papers: [17], [19], [20], [3], [4], [2], [16], [5], [1], [18], [9], [11], [12], [8], [6], [7], [13], [10], [21], [14], and [15]. For simplicity, we use the following convention: X denotes a Banach algebra, p denotes a real number, w, z, z1, z2 denote elements of X, k, l, m, n denote natural numbers, s1, s2, s3, s, s ′ denote...

Let X,Y be locally convex spaces and L(X,Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series P Tk in L(X,Y ). First, if λ is a scalar sequence space, we say that the series P Tk is λ multiplier convergent for a locally convex topology τ on L(X,Y ) if the series P tkTk is τ convergent for every t = {tk} ∈ λ. We establish...