Intermediate Classes of Nuclear Multilinear Operators

Abstract

AbstractThis paper introduces the class of $$\left( p_1,\ldots ,p_m,\sigma ,q,\nu \right) $$ p 1 , … , p m , σ , q , ν -nuclear m-linear operators between Banach spaces, as an intermediate space between the class of nuclear multilinear operators and the whole class of all bounded multilinear operators. The connection with the theory of summing m-linear operators is established. Moreover, we identify this space with a dual space by means of a reasonable crossnorm inspired by the Chevet–Saphar norm.