An Analysis upon Organization of Some Nuclear Mappings and Quasi-Nuclear Mappings

Abstract

In this paper we sum up the notable outcome which says that the arrangement of semi nuclear maps is nuclear. All the more accurately, we characterize what we call a 2-quasi?-nuclear guide between normed spaces and we say that the organization of a 2-semi ?-nuclear guide with a semi ?-nuclear guide is a pseudo-?-nuclear guide. Additionally, we say that a semi ?-nuclear guide is a 2-semi ?-nuclear guide. For a nuclear G?-space, we say that a straight guide T between normed spaces is 2-semi ?-nuclear if and only if it is semi ?-nuclear. We present new kind of maps between normed spaces to be specific, p-quasi?-nuclear guide. We say that the piece of a q-semi ?-nuclear guide (0 < q ? 1) with a p-semi ?-nuclear guide (0 < p ? 1) is a pseudo-?-nuclear guide. Additionally we say that for a nuclear G?-space a direct guide T between normed spaces isp-semi ?-nuclear iff it is q-semi ?-nuclear.