Complex Geodesics on Convex Domains

Sean Dineen; Richard M. Timoney

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arXiv · 0907.1194

Complex Geodesics on Convex Domains

Sean Dineen·Richard M. Timoney

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Abstract

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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BibTeX RIS

Sean Dineen, Richard M. Timoney. 2009-07-07. Complex Geodesics on Convex Domains. https://arxiv.org/abs/0907.1194

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