Analytic functions whose range is dense in a ball
Analytic functions whose range is dense in a ball
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范围密集的球状解析函数
DOI：
10.1016/0022-1236(76)90021-5
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
J. Globevnik
中科院分区：
文献类型：
--
作者：
J. Globevnik
用Δ表示。Δ)打开（回复）设E是单位圆T的一个封闭子集，设F是Lesbesgue测度为0的T−E的一个相对封闭子集。证明了以下结果。给定复巴拿赫空间X和一个有界连续函数f: f→X，存在一个f的扩展，在\ \ gD−E上有界连续，在Δ上解析，满足sup{‖f′(z)‖：zε Δ−E，这证明了对于任意可分复巴拿赫空间X，存在一个解析函数，从Δ到X，其值域包含在X的单位球内且密集。
Denote by Δ (resp. Δ) the open (resp. closed) unit disc in C. Let E be a closed subset of the unit circle T and let F be a relatively closed subset of T− E of Lesbesgue measure zero. The following result is proved. Given a complex Banach space X and a bounded continuous function f: F→ X, there exists an extension f̃ of f, bounded and continuous on\̄ gD− E, analytic on Δ and satisfying sup {‖ f ̃ (z)‖: zε δ− E. This is applied to show that for any separable complex Banach space X there exists an analytic function from Δ to X whose range is contained and dense in the unit ball of X.