Representation of sequence classes by operator ideals: Part II

Abstract

In this paper we continue the investigation of classes of vector-valued sequences that are represented by Banach operator ideals. By a procedure we mean a correspondence \(X \mapsto X^{\textrm{new}}\) that assigns a sequence class \(X^{\textrm{new}}\) built upon a given sequence class X. The general question is whether or not \(X^{\textrm{new}}\) is ideal-representable whenever X is. We address this question for three already studied procedures, namely, \(X \mapsto X^{\textrm{u}}\), \(X \mapsto X^{\textrm{dual}}\) and \(X \mapsto X^{\textrm{fd}}\). Applications of the solutions of these problem will provide new concrete examples of ideal-representable sequence classes.