局部凸空间的一致凸性

本文对局部凸空间引进了一致凸,拓扑一致凸的概念。证明了亚完备的拓扑一致凸的局部凸空间是半自反的。     

Approximation of Convex Bodies by ConvexBodies

For the affine distance d(C,D) between two convex bodies C, D(?) Rn, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) < n1/2 if one is an ellipsoid and another is symmetric, d(C, D) < n if both are symmetric, and from F. John's result and d(C1,C2) < d(C1,C3)d(C2,C3) one has d(C,D) < n2 for general convex bodies; M. Lassak proved d(C, D) < (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.