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A Note on Extreme Points in Dual Spaces

A Note on Extreme Points in Dual Spaces
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摘要 Given a normed space X it can be easily proven that every extreme point in Bx＊, the unit ball of X＊, is the restriction of an extreme point in Bx Our purpose is to study when the restrictions of extreme points in Bx＊＊＊ are extreme points in Bx＊. Namely, we characterize Ll-preduals satisfying the aforementioned property. Given a normed space X it can be easily proven that every extreme point in Bx＊, the unit ball of X＊, is the restriction of an extreme point in Bx Our purpose is to study when the restrictions of extreme points in Bx＊＊＊ are extreme points in Bx＊. Namely, we characterize Ll-preduals satisfying the aforementioned property.
作者 Juan Francisco MENA-JURADO Juan Carlos NAVARRO-PASCUAL
机构地区 Departamento de Análisis Matemático Departamento de lgebra y Análisis Matemático
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第3期471-476,共6页 数学学报（英文版）
基金 Supported by Ministerio de Ciencia e Innovación and Junta de Andalucía Projects (Grant Nos. MTM2009-07498, MTM2010-17687 and FQM-3737)
关键词 Extreme point Ll-predual M-IDEAL Extreme point, Ll-predual, M-ideal
分类号 O177 [理学—基础数学]
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参考文献12

  • 1Blumenthal, R. M., Lindenstrauss, J., Phelps, R. R.: Extreme operators into C (K). Pacific J. Math., 15, 747-756 (1965).
  • 2Sharir, M.: Extremal structure in operator spaces. Trans. Amer. Math. Soc., 186, 91-111 (1973).
  • 3Harmand, P., Werner, D., Werner, W.: M-ideals in Banach Spaces and Banach Algebras. Lecture Notes in Math., 1547, Springer-Verlag, Berlin, 1993.
  • 4Lima, .: Intersection properties of balls in spaces of compact operators. Ann. Inst. Foumer, 28, 35-65 (1978).
  • 5Mena-Jurado, J. F., Montiel-Aguilera, F.: A note on nice operators. J. Math. Anal. Appl., 289, 30-34 (2004).
  • 6Dutta, S., Rao, T. S. S. R. K.: On weak*-extreme points in Banach spaces. J. Convex Anal., 10, 531-539 (2003).
  • 7Gendler, A.: Extreme operators in the unit ball of L (C(X),C(Y)) over the complex field. Proc. Amer. Math. Soc., 57, 85-88 (1976).
  • 8Lacey, H. E.: The Isometric Theory of Classical Banach Spaces, Springer-Verlag, Berlin-New York, 1974.
  • 9Lindenstrauss, J., Wulbert, D. E.: On the classification of the Banach spaces whose duals are Ll-spaces. J. Funct. Anal., 4, 332-349 (1969).
  • 10Lazar, A. J., Lindenstrauss, J.: Banach spaces whose duals are Ll-Spaces and their representing matrices. Acta Math., 126, 165-193 (1971).
Acta Mathematica Sinica,English Series
2013年 第3期

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