凸区域上的复测地线
Complex Geodesics on Convex Domains
摘要：
研究了巴拿赫空间$X$中连接凸有界域上两点的复测地线的存在唯一性。在假设$X$在其双对偶中1-可补的条件下，证明了$X$的单位球的存在性.证明了taut域的另一个存在性结果。证明了具有解析Radon-Nikodym性质的空间中严格凸有界域的唯一性。如果$X$的单位球具有在0处幂型衰减的复一致凸模，则单位球中的所有复测地线满足利普希茨条件。将所得结果应用于经典巴拿赫空间，给出了数列空间$\ell^p$（$1 \leq p < \infty$）的单位球上所有复测地线的一个公式.
英文摘要：
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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