ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: Kadets, V. M., and L. M. Tseytlin, O. I. Vladimirskaya, Kharkov State University, Kharko v, Ukraine The Lyapunov property of certain Banach spaces The well-known Lyapunov theorem states that the range of a countablyadditive atomless measure with values in a finite-dimensional space is convex. Since this theorem does not hold in any infinite-dimensional Banach space, generalizations to such spaces usually consider the closure of the measure’s range. A Banach space is said to have the Lyapunov property, if the closure of the range of any countably-additive atomless measure with values in this space is convex. The results on the Lyapunov property of several Banach spaces will be presented. Spaces c_{0}(Γ, X), C(K) where K is a countable compact are shown to have the Lyapunov property, as well as spaces of Tsirelson, Schlumprecht, Gowers-Maurey, Gowers. References: V. M. Kadets, G. Schechtman. The Lyapunov Theorem for l_{p}-valued Measures. St. Petersburg Math. J. , Vol. 4 (1993), No. 5, p. 961–966. L. M. Tseytlin, O. I. Vladimirskaya. On the Lyapunov property of certain Banach spaces. Proc. of Institute of Mathematics of Ukrainian Nationa l Academy of Sciences, issue 2(18), 1998.