Limiting Case for Interpolation Spaces Generated by Holomorphic Semigroups

tA

)_t≥0 on X. We denote by X_A(θ,p), for 0 < θ < 1, the interpolation spaces of X and D(A) introduced by Berens and Butzer in [1]. These spaces play an important role in the approximation theory ( [2] ) as well as in the study of the abstract parabolic equation u′ (t) = Au(t) + f(t) ( [3] ). It has been proved in [6] that these spaces are meaningful (and still enjoy relevant properties) also in the case θ = 0. In this paper we continue the study of [6] and prove new interesting properties of these spaces.