变换函数Φ及KUR空间存在固定点的条件
The Transformation Function Φ and the Condition Needed for KUR Space Having the Fixed Point
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摘要: 近年来,在研究外延Banach空间性质上取得了进展的有:1979年SuilliVan讨论实LP(x)空间性质并采用二维子空间的一致状态,定义了KUR空间的概念;1980年Huff讨论用序列定义的广义一致凸性,引用了NUC空间的概念:1982年俞鑫泰断言:KUR空间就是NUC空间的证明[1]。而值得注意的是Suillivan及Huff又分别提出了十分有趣的问题如下:是否每一个上自反空间都存在一个不动点[2]?及在什么条件下LP(x)空间是NUC空间[3]? 本文旨在研究变换函数的性质[4]及其与上述两个问题的关系。Abstract: In the last several years some progress has been made in the study of the properties of the extent of Banaeh space: In 1979, for example, when SuiIIivan discussed a related characterization of real LP(x) space,he used uniform behavior of all two-dimensional subspace and defined this concept of a KUR space; In 1980 Huff used the concept of an NUC space when he discussed the property of generalizing uniform convexity which was defined in terms of sequence; And in 1984 Yu Xin-tai(俞鑫泰)stated certainly and proved that the RKU space is equal to the NUC space[1]. However, the following quite interesting questions raised by Suillivan and Huff merit attention; Does every super-reflexive space have the fixed point propertyyand what conditions are needed for an LP(x) space to be NUC space[3]? respectively. The purpose of this paper is to study the characterization of transformation functionary and relationships between transformation function [4] and the two questions above.
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[1] 俞鑫泰,科学通报,24 (1982), 1473-1475. [2] Suilli}an, F, Can,J.Math,31,3 (1979),628-636. [3] Huff, R,Rocky Motain, J.Math,10. 4 (1980),743-479. [4] 谷安海,东北工学院学报,3 (1983),15-20. [5] Schechter, M,Principles of functional Analysis,-Academic Press, New York and London, p4-57,208-209. [6] James, R, C, Isral, I, Math,2 (1964),101-119. [7] 谷安海,力学与实践,2 (1984),27-31. [8] Harlshore, R,Algebraic Geometry, Spring-Verlag, New York-Heidelberg-Berlin(1977), 1-2. -
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