RANDOMIZED SERIES AND GEOMETRY OF BANACH SPACES

作者：Lee Han Ju^*

来源：Taiwanese Journal of Mathematics, 2010, 14(5): 1837-1848.

DOI：10.11650/twjm/1500406019

• Representability
• Extreme point
• Strict convex
• Midpoint locally uniformly convex
• Uniformly convex
• Upper locally uniformly monotone
• Uniformly monotone

We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n >= 2 and 1 < p < infinity, it is shown that l(infinity)(n) is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner L(p)(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is uniformly monotone if and only if its p-convexification E((P)) is uniformly convex and that a Kothe function space E is upper locally uniformly monotone if and only if its p-convexification E((P)) is midpoint locally uniformly convex.

• 出版日期2010-10