(t-)orthogonality in p-adic Banach spaces

Sabine Borrey
1995 Annales mathématiques Blaise Pascal  
Let (E, ~ . ~) be a Banach space over K. We shall prove that orthogonality in E can be expressed in terms of distances to convex hulls of points in E instead of distances to the linear hulls of these same points, which gives in fact a new characterization of orthogonality. Also, for an absolutely convex, weakly c'-compact subset of a Banach space having the Hahn-Banach extension property, an equivalent condition is given for the compactoidness of the set.
doi:10.5802/ambp.20 fatcat:5ph2qqthfjhopmtrspega6zrha