Complex convexity and finitely additive vector measures

Lešnjak, Gorazd

doi:10.1090/S0002-9939-1988-0934858-9

Complex convexity and finitely additive vector measures
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Proc. Amer. Math. Soc. 102 (1988), 867-873 Request permission

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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