Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Some interpolation results that are the exclusive property of compact operators

Fernando Cobosa1, Luz M. Fernández-Cabreraa2, Antón Martíneza3 and Evgeniy Pustylnika4

a1 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid 28040 Madrid, Spain (cobos@mat.ucm.es)

a2 Sección Departamental de Matemática Aplicada, Escuela de Estadística, Universidad Complutense de Madrid 28040 Madrid, Spain (luzfer@nfssrv.mat.ucm.es)

a3 Departamento de Matemática Aplicada, ETS Ingenieros Industriales, Universidad de Vigo, 36200 Vigo, Spain (antonmar@uvigo.es)

a4 Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel (evg@techunix.technion.ac.il)

Abstract

We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J-functionals of interpolation theory.

(Received December 06 2000)

(Accepted April 12 2001)