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Complex convexity and finitely additive vector measures

Author: Gorazd Lešnjak
Journal: Proc. Amer. Math. Soc. 102 (1988), 867-873
MSC: Primary 46B20; Secondary 28B05, 46G10, 47D15
MathSciNet review: 934858
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Abstract: We prove that complex uniform convexity of a complex normed space $ X$ is equivalent to complex uniform convexity of $ \operatorname{bva} {\text{(}}\mathcal{F}{\text{,X)}}$. Similar results hold also for complex uniform convexity at a point. Some consequences for duals of certain operator spaces are discussed.

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Keywords: Vector measures, compact operators, complex extreme points, tensor products
Article copyright: © Copyright 1988 American Mathematical Society

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