The <i>α_σ</i>-Approximation Property and Its Related Operator Ideals

Abstract

In this paper, we study the σ-tensor norm (ασ), the absolutely τ-summing operator and the σ-nuclear operator. We characterize the ασ-approximation property in terms of some density of the space of absolutely τ-summing operators. When X* or Y*** has the approximation property, we prove that an operator T from X to Y is σ-nuclear if the adjoint of T is σ-nuclear.

Keywords

• tensor norm
• approximation property
• operator ideal