臺灣博碩士論文加值系統

摘要
在這份論文中，我們將特殊凸體：單位閉體的Lk-UR性一般化到一般的凸體，且證明所有建立在單位閉球的古典結果也對於一般的閉凸集合成立，我們也以序列，邊界或是移動重心的觀點爲Lk-UR集合提供了一些等價的形式。

Abstract
In this thesis﹐we introduce the notion of Lk-UR property from the specific convex body：the closed unit ball to the general convex bodies in a Banach space and prove thatall the classical results established for the closed unit ball also holds for the general
closed convex sets. We also offer several equivalent forms of Lk-UR sets in terms of sequences﹐boundary﹐or removing the barycenter.

Contents

1 Introduction 1
2 Gauge function and volume of simplex body 1
3 Lk-UR sets 8
4 Characterizations of Lk-UR sets 12

References 18

References
【1】James A.Clarkson：Uniformly convex spaces﹐Trans. Amer.Math. Soc. Vol.40（1936）﹐396-414.
【2】Chao-Xun Nan and Jian-Hua Wang：On the Lk-UR and LkR spaces﹐Math. Proc. Camb. Phil. Soc. 104（1988）﹐521-526.
【3】Jia-yu Shiu: Relationships among k-UR﹐k-NUR﹐and kR. Master Thesis﹐Fu Jen Catholic University（1993）.
【4】Francis Sullivan：A generalization of uniformly rotund Banach space﹐Canad.J.Math.Vol.31﹐No.3（1979）﹐628-636.