Weakly $p$-nuclear bilinear operators

Abstract

The purpose of this article is to investigate the class of weakly $p$-nuclear bilinear operators between Banach spaces. This notion extends the classical theory of nuclear operators introduced by A. Grothendieck, as well as its multilinear generalizations developed by A. Pietsch and others. In particular, we characterize weakly $p$-nuclear bilinear operators through appropriate tensor norms, showing that the space of such operators forms a Banach ideal and analyzing some of its structural properties. Moreover, in the context of duality theory for these operator spaces, we introduce the class of quasi-Cohen $p$-nuclear bilinear operators and establish a Pietsch-type domination theorem.