A subscription is required to access this article.
Let be the Banach space of functions on bounded together with all derivatives of order and with derivatives of order having moduli of continuity for some . Let be the trace space to a closed subset . The geometric predual of is the minimal closed subspace of the dual containing evaluation functionals of points in . We study geometric properties of spaces and their relations to the classical Whitney problems on the characterization of trace spaces of functions on . In particular, we show that each is a complemented subspace of , describe the structure of bounded linear operators on , prove that has the bounded approximation property and that in some cases space is isomorphic to the second dual of its subspace consisting of restrictions to of functions with compact supports.
Cite this article
Alexander Brudnyi, On properties of geometric preduals of spaces. Rev. Mat. Iberoam. 35 (2019), no. 6, pp. 1715–1744DOI 10.4171/RMI/1099