On operator ideals using weighted Cesàro sequence space

Abstract

Let s=(sn) be a sequence of s-numbers in the sense of Pietsch. In this paper we have introduced a class Ap,q(s) of s-type ces(p,q) operators by using weighted Cesàro sequence space for 1<p<∞. It is shown that the class Ap,q(s) forms a quasi-Banach operator ideal. Moreover, the inclusion relations among the operator ideals as well as the inclusion relations among their duals are established. Finally, we have proved that the class Ap,q(a) of approximation type ces(p,q) operators is small.

Keywords

• s-Numbers
• Approximation numbers
• Operator ideals
• Sequence space