math.FA — Functional Analysis
The Daugavet Property of Bidual Spaces
We construct a separable Banach space whose bidual has the Daugavet property. The construction proceeds by successively extending finite-dimensional spaces so that prescribed vectors are approximated by averages of newly added unit vectors. A simultaneous extension argument produces finitely many fixed functionals whose norm-attaining faces approximate the unit ball of the bidual.
A mix of human-written and AI-generated textHuman understanding: all partsBidualDaugavet property