Invertibility of Operators in Spaces of Real Interpolation

Abstract

Let A be a linear bounded operator from a couple X = (X0 , X1 ) to a couple Y = (Y0 , Y1 ) such that the restrictions of A on the spaces X0 and X1 have bounded inverses. This condition does not imply that the restriction of A on the real interpolation space (X0 , X1 ),q has a bounded inverse for all values of the parameters and q . In this paper under some conditions on the kernel of A we describe all spaces (X0 , X1 ),q such that the operator A : (x0 , X1 ),q (Y0 , Y1 ) has a bounded inverse.