A note on the Mackey-star topology on a dual Banach space

详细信息    查看全文

• 作者：A. J. Guirao ; V. Montesinos
• 关键词：Analytic space ; Mackey ; star topology ; Strongly weakly compactly generated space ; Banach space ; Primary 46B20 ; Secondary 46B03 ; 46B10
• 刊名：Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：109
• 期：2
• 页码：417-418
• 全文大小：317 KB
• 参考文献：1.Fabian, M., Montesinos, V., Zizler, V.: On weak compactness in \(L_1\) spaces. Rocky Mt. J. Math. 39, 1885-893 (2009)MATH MathSciNet View Article
  2.Grothendieck, A.: Topological vector spaces, Translated from the French by Orlando Chaljub. Gordon and Breach Science publishers, New York (1973)
  3.K?kol, J., López-Pellicer, M.: On realcompact topological vector spaces. RACSAM 105, 39-0 (2011)View Article
  4.K?kol, J., Kubi?, W., López-Pellicer, M.: Descriptive Topology in Selected Topics of Functional Analysis. In: Developments in Mathematics, vol. 24. Springer, New York (2011)
  5.Kirk, R.B.: A note on the Mackey topology for \((C^b(X)^*, C^b(X))\) . Pac. J. Math. 45(2), 543-54 (1973)MATH MathSciNet View Article
  6.K?the, G.: Topological vector spaces I, Translated by D.J.H. Garling, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 159, 2nd edn. Springer, New York (1969)
  7.Schlüchtermann, G., Wheeler, R.F.: On strongly WCG Banach spaces. Math. Z. 199, 387-98 (1988)MATH MathSciNet View Article
  
• 作者单位：A. J. Guirao (1)
  V. Montesinos (1)
  
  1. Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022, Valencia, Spain
  
• 刊物类别：Mathematics and Statistics
• 出版者：Springer Milan
• ISSN：1579-1505

文摘

By using a result in Kirk (Pac J Math 45:543-54, 1973), we show that there are separable Banach spaces such that their dual spaces, endowed with the Mackey-star topology, are not analytic. This solves a question raised in K?kol et al. (Descriptive topology in selected topics of functional analysis, Springer, 2011), and in K?kol and López-Pellicer (RACSAM 105:39-0, 2011).