Interpolation of compact non-linear operators on Banach triples. (English) Zbl 1119.46301

Cofan, Nicolae; Stan, Ilie

An. Univ. Craiova, Ser. Mat. Inf. 33, 1-7 (2006).

Summary: We investigate the behavior of Lipschitz and compact non-linear operators under \(K\) and \(J\) real interpolation methods for Banach triples. We begin with the case when one of the triples reduces to a single Banach space, and we prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz and compact non-linear operators. We also establish a compactness result when the interpolation operator is considered from a \(J\)-space into a \(K\)-space.

MSC:

46B70

Interpolation between normed linear spaces

Keywords:

interpolation; compact non-linear operators