Interpolation of a measure of weak non-compactness

Abstract

Abstract. We study the measure of weak non-compactness of operators between abstract interpolation spaces. We prove an estimate of this measure, depending on the fundamental function of the space. We specialize our results and show applications to weak compactness of operators.

On interpolation of weakly compact bilinear operators

“…A quantitative approach based on the measure of weak noncompactness γ was undertaken by Kryczka, Prus and Szczepanik [29] and further developed by Kryczka and Prus [28], covering the case of complex interpolation of weakly compact operators. Other results in this direction can be seen in the papers by Fan [19] and Szwedek [40].…”

Extrapolation properties of closed operator ideals

“…More details on these characterizations can be found in [7] and [14], where the ideal measures that they define are studied and their interpolation properties are shown (see also [27] …”