Resumen de On properties of geometric preduals of Ck,ω spaces

Alexander Brudnyi

• Let Ck,ωb(Rn) be the Banach space of Ck functions on Rn bounded together with all derivatives of order ≤k and with derivatives of order k having moduli of continuity O(ω) for some ω∈C(R+). Let Ck,ωb(S):=Ck,ωb(Rn)|S be the trace space to a closed subset S⊂Rn. The geometric predual Gk,ωb(S) of Ck,ωb(S) is the minimal closed subspace of the dual (Ck,ωb(Rn))∗ containing evaluation functionals of points in S. We study geometric properties of spaces Gk,ωb(S) and their relations to the classical Whitney problems on the characterization of trace spaces of Ck functions on Rn. In particular, we show that each Gk,ωb(S) is a complemented subspace of Gk,ωb(Rn), describe the structure of bounded linear operators on Gk,ωb(Rn), prove that Gk,ωb(S) has the bounded approximation property and that in some cases space Ck,ωb(S) is isomorphic to the second dual of its subspace consisting of restrictions to S of C∞(Rn) functions with compact supports.