Pietsch [5] introduced the concept of absolutely summing operators in Banach spaces and later in [6] extended this concept to absolutely p-summing operators. At the background of these concepts are the sequence spaces I p and their duality theory. The object of the present paper is to extend the above concept to abstract sequence spaces 2. The sequence spaces 2 involved are described in Section...

where B = (bn)n≥1 is a one-column matrix and X the unknown, see [1, 2, 3, 4, 5, 6, 7, 8, 10]. Equation (1.2) can be written in the form AX = B, where AX = (An(X))n≥1. In this paper, we will also consider A an operator from a sequence space into another sequence space. A Banach space E of complex sequences with the norm ‖‖E is a BK space if each projection PnX = xn is continuous for all X ∈ E. A...