Invertibility of Operators in Spaces of Real Interpolation

Résumé

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)θ,q has a bounded inverse for all values of the parameters θ and q. In this paper under some conditions on the kernel of A we describe all spaces (X0,X1)θ,q such that the operator A : (x0,X1)θ,q → (Y0,Y1) has a bounded inverse.