| 在Banach空间中推广的Roper-Suffridge算子(Ⅰ) |
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| 引用本文： | 朱玉灿,刘名生.在Banach空间中推广的Roper-Suffridge算子(Ⅰ)[J].数学学报,2007(1). |
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| 作者姓名： | 朱玉灿 刘名生 |
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| 作者单位： | 福州大学数学系，华南师范大学数学科学学院 福州 350002，广州 510631 |
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| 基金项目： | 高等学校博士点基金(20050574002)，福建省自然科学基金(Z0511013)，福建省教育厅基金(JA02146) |
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| 摘 要： | 本文将Cn中的Roper-Suffridge算子推广到任意复Banach空间中,并证明这种算子在任意复Banach空间中的某些区域上具有保持ε星形性,由此可以构造出任意复Banach空间,复Hilbert空间和Cn中的一些区域上的许多双全纯星形映照、双全纯凸映照、双全纯ε星形映照,同时,得到它们的增长定理等,将龚升与刘太顺,Roper与suffridge,Graham,Kohr等学者在Cn中的一些结果推广到任意复Banach空间或复Hilbert空间中．
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| 关 键 词： | 双全纯凸映照 双全纯星形映照 双全纯ε星形映照 |
The Generalized Roper-Suffridge Extension Operator in Banach Spaces (Ⅰ) |
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| Yu Can ZHU.The Generalized Roper-Suffridge Extension Operator in Banach Spaces (Ⅰ)[J].Acta Mathematica Sinica,2007(1). |
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| Authors: | Yu Can ZHU |
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| Institution: | Yu Can ZHU Department of Mathematics,Fuzhou University,Fuzhou 350002,P. R. China Ming Sheng LIU School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P. R. China |
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| Abstract: | In this paper, we extend the Roper-Suffridge extension operator from Cn to a complex Banach space X. It is proved that this operator preserves the e starlikeness on some domains in the complex Banach space. Prom these, we may construct a lot of concrete examples about biholomorphic starlike mappings, biholomorphic convex mappings, biholomorphicεstarlike mappings on some domains in Cn, or complex Hilbert spaces, or complex Banach spaces from e starlike functions on the unit disc U in C. Meanwhile, the growth theorems of the corresponding mappings are given. Some results of Gong and Liu, Roper and Suffridge, Graham, Kohr and others in Cn are extended to complex Hilbert spaces or complex Banach spaces. |
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| Keywords: | biholomorphic convex mapping biholomorphic starlike mapping biholo-morphicεstarlike mapping |
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