Interpolation of Compact-Operators: The Multidimensional Case

Abstract

We investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated operators, examples, characterization as Aronszajn-Gagliardo functors,.... We also describe the relationship between Sparr and Fernandez methods and we derive sharp estimates for the norms of interpolated operators in Fernandez' case. Then we investigate the behaviour of compact operators. We begin with the case when one of the N-tuples reduces to a single Banach space, and later we treat the general case by means of the approach developed in [8].