On a separable weak version of the bounded approximation property

被引：0
作者：
Eve Oja
机构：
[1] University of Tartu,Institute of Mathematics and Statistics
[2] Estonian Academy of Sciences,undefined
来源：
Archiv der Mathematik | 2016年 / 107卷
关键词：
Banach spaces; Bounded approximation properties; Separability; Primary: 46B28; Secondary: 46B20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Recently, Lee introduced and studied the separable weak bounded approximation property (BAP). Lee proved that the separable weak BAP of X∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X^*}$$\end{document}, the dual space of a Banach space X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X}$$\end{document}, coincides with the BAP of X∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X^*}$$\end{document} whenever X∗∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X^{**}}$$\end{document} has the weak Radon–Nikodým property. We show that the separable weak BAP and the BAP are always the same properties.
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页码：185 / 189
页数：4
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共 21 条
  • [1] Enflo P.(1973)A counterexample to the approximation problem in Banach spaces Acta Math. 130 309-317
  • [2] Figiel T.(1973)The approximation property does not imply the bounded approximation property Proc. Amer. Math. Soc. 41 197-200
  • [3] Johnson W. B.(1982)Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces Studia Math. 73 225-251
  • [4] Heinrich S.(1972)A complementary universal conjugate Banach space and its relation to the approximation problem Israel J. Math. 13 301-310
  • [5] Mankiewicz P.(2012)Dual spaces of compact operator spaces and the weak Radon–Nikodým property Studia Math. 210 247-260
  • [6] Johnson W. B.(2015)The separable weak bounded approximation property Bull. Korean Math. Soc. 52 69-83
  • [7] Lee K. Y.(2010)Bounded approximation properties via integral and nuclear operators Proc. Amer. Math. Soc. 138 287-297
  • [8] Lee K. Y.(2012)Bounded approximation properties in terms of Math. Scand. 110 45-58
  • [9] Lima Å.(2005)The weak metric approximation property Math. Ann. 333 471-484
  • [10] Lima V.(2006)The impact of the Radon-Nikodým property on the weak bounded approximation property Rev. R. Acad. Cien. Serie A. Mat. 100 325-331
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