Null sequences: a unified point of view

LASSALLE, S.

Kent - OHIO

Congreso; Infinite Dimensional Analysis: Celebrating Richard Aron's Work and Impact; 2016

Let A be a Banach operator ideal and 𝑋 be a Banach space. We undertake the studyof the vector space of A-null sequences of Carl and Stephani on 𝑋, from aunified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (𝓁1;𝑋), the space of A-null sequences behaves much alike 𝑐0(𝑋). When this is the case we give a geometric tensor product representation of the space of-A null sequences. On the other hand, weshow an example where the representation fails. Also, via a trace duality formula, we characterize the dual space.