A quantitative approach to weak noncompactness in interpolation and extrapolation of operators

Линиите свързват координатора с партньорите.

Накратко на български

Цел на проекта

The main objective of the proposed research is the thorough study of the behavior of weakly noncompact operators under interpolation and extrapolation. The research is concentrated on the following problem: To which degree can weak noncompactness of an operator be interpolated and extrapolated? The investigations would involve both the real and complex interpolation methods for families of Banach spaces and contemporary extrapolation methods. We propose a quantitative approach to weak no compactness. We consider special serminorms which determine the deviation of a given operator from weak compactness. The quantitative approach gives also qualitative results for weakly compact operators. Due to recently published results the existence of quantitative results depends on the way of measuring noncompactness. We deal with the new measures of weak noncompactness which are invariant under linear isometries and which succeeded in classical interpolation for pairs of Banach spaces. Compactness with respect to various topologies is one of the most important property broadly used in many applications of analysis. However, many results still hold if we assume some deviation from compactness. Both interpolation and extrapolation deal with operators which act on families of spaces. In such general situations the expected results can be applied.

Оригинален текст от CORDIS (на английски).

Участници

• UNIVERSIDAD COMPLUTENSE DE MADRID · MADRIDКоординаторИспания

Връзки

• Виж в CORDIS