Measure of non-compactness and Sparr’s interpolation methods. (English) Zbl 1199.46165

Bărbătei, O.; Cofan, Nicolae; Stan, Ilie; Hedrea, Ciprian

An. Univ. Vest Timiș., Ser. Mat.-Inform. 46, No. 2, 13-24 (2008).

Summary: We establish an estimate for the measure \(\beta (T)\) of non-compactness of an operator \(T\) acting from some intermediate spaces \(A\) with respect to Banach \(n\)-tuples \(\overline A\) into some intermediate space \(B\) with respect to Banach \(n\)-tuples \(\overline B\). We begin with the case when one of the \(n\)-tuples is reduced to a single Banach space and, later, we will treat the general case.

MSC:

46M35	Abstract interpolation of topological vector spaces
46B70	Interpolation between normed linear spaces

Keywords:

interpolation methods; interpolation of compact operators