SOME RESULTS OF OPERATOR IDEALS ON s-TYPE |A, p| OPERATORS

Let s = (s(n)) be a sequence of s-numbers in the sense of Pietsch and A be an infinite matrix. This paper presents a generalized class A((s))-p of s-type |A, p| operators using s-number sequence which unifies many earlier well known classes. It is shown that the class A((s)) - p forms a quasi-Banach operator ideal under certain conditions on the matrix A. Moreover, the inclusion relations among the operator ideals as well as the inclusion relations among their duals are established. It is also proved that for the Ces` aro matrix of order 1, the operator ideal formed by approximation numbers is small for 1 < p < infinity.