Abstract
In this paper, we examine the Radon-Nikodym property and its relation to the Bishop-Phelps theorem for complex Banach spaces. We also show that the Radon-Nikodym property implies the Bishop-Phelps property in the complex case.
Highlights
Let X be a complex Banach space and let C be a closed convex subset of X
We will show that the unit ball of an infinite-dimensional function algebra has no strongly exposed points
Lomonosov [4] constructed a closed, bounded, and convex subset C of a complex Banach space such that the set of support points of C is empty. This means that the Bishop-Phelps theorem fails to hold in the complex case
Summary
We examine the Radon-Nikodym property and its relation to the Bishop-Phelps theorem for complex Banach spaces.
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