Directionally Euclidean structures of Banach spaces

• Autorzy: Jarno Talponen
• Języki publikacji: EN

Abstrakty

EN

We study Banach spaces with directionally asymptotically controlled ellipsoid-approximations of the unit ball in finite-dimensional sections. Here these ellipsoids are the unique minimum volume ellipsoids, which contain the unit ball of the corresponding finite-dimensional subspace. The directional control here means that we evaluate the ellipsoids by means of a given functional of the dual space. The term 'asymptotical' refers to the fact that we take 'lim sup' over finite-dimensional subspaces.
This leads to isomorphic and isometric characterizations of Hilbert spaces. An application involving Mazur's rotation problem is given. We also discuss the stability of the family of ellipsoids as the dimension and geometry vary. The methods exploit ultrafilter techniques and we also apply them in conjunction with finite Auerbach bases to study the convexity properties of the duality mappings.

Kategorie tematyczne

• 52A23: Asymptotic theory of convex bodies
• 43A35: Positive definite functions on groups, semigroups, etc.
• 46C15: Characterizations of Hilbert spaces
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 202
• Numer: 2
• Strony: 191-203

Daty

wydano

2011

Twórcy

autor

Jarno Talponen

• Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland

Identyfikatory

DOI

10.4064/sm202-2-5