Complex Geodesics on Convex Domains

Details Complex Geodesics on Convex Domains Complex Geodesics on Convex Domains

2009-07-07

arxiv.org/abs/0907.1194v1

Progress in Functional Analysis, North Holland Mathematical Studies, 170, 333--365, 1992

Mathematics

Functional Analysis

Due to a typographical fault, the bars over letters in the published version of this article did not appear and this rendered

Scientific paper

Existence and uniqueness of complex geodesics joining two points of a convex bounded domain in a Banach space $X$ are considered. Existence is proved for the unit ball of $X$ under the assumption that $X$ is 1-complemented in its double dual. Another existence result for taut domains is also proved. Uniqueness is proved for strictly convex bounded domains in spaces with the analytic Radon-Nikodym property. If the unit ball of $X$ has a modulus of complex uniform convexity with power type decay at 0, then all complex geodesics in the unit ball satisfy a Lipschitz condition. The results are applied to classical Banach spaces and to give a formula describing all complex geodesics in the unit ball of the sequence spaces $\ell^p$ ($1 \leq p < \infty$).

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