On the smoothness of \(L^p\) of a positive vector measure

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• 作者：L. Agud ; J. M. Calabuig ; E. A. Sánchez-Pérez
• 关键词：Banach function spaces ; Norm attaining functionals ; Operators ; Primary 46E30 ; Secondary 47B38 ; 46B42 ; 46B28
• 刊名：Monatshefte f篓鹿r Mathematik
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：178
• 期：3
• 页码：329-343
• 全文大小：424 KB
• 参考文献：1.Beauzamy, B.: Introduction to Banach Spaces and Their Geometry. North-Holland, Amsterdam (1982)MATH
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• 作者单位：L. Agud (1)
  J. M. Calabuig (2)
  E. A. Sánchez-Pérez (2)
  
  1. Departamento de Matemática Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022?, Valencia, Spain
  2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022?, Valencia, Spain
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081

文摘

We investigate natural sufficient conditions for a space \(L^p(m)\) of \(p\)-integrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth. We give also some examples and show some applications of our results for determining norm attaining elements for operators between two spaces \(L^p(m_1)\) and \(L^q(m_2)\) of positive vector measures \(m_1\) and \(m_2\). Keywords Banach function spaces Norm attaining functionals Operators