The <i>g_E</i>-Approximation Property Determined by the Banach Space <i>E</i> = <i>ℓ_q</i>(<i>ℓ_p</i>)

Abstract

We study the gE-approximation property for the Banach space E=ℓq(ℓp), which is an extension of Saphar’s p-approximation property. We establish some characterizations of the gE-approximation property using the space of E-summing operators, which is an extension of the space of p-summing operators.

Keywords

• schauder basis
• vector-valued sequence
• tensor norm
• operator ideal
• approximation property