Abstract
We apply the notion of Banach space operator ideals in nuclear spaces through
topological vector spaces. The motivation for this study came from attempts to
generalize the structure of nuclear spaces as a result of nuclear maps from
functional analysis context. The compact closed structure associated with the
category of relations results to nuclear ideals. Basic properties of Banach
space operator ideals in relation to the structure of nuclear spaces will be
demonstrated. We therefore establish a close correspondence between
Banach space operator ideals and nuclear ideals through topological vector.