Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

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• 作者：Pilar Rueda ; Enrique A. Sánchez-Pérez
• 关键词：46E30 ; 47B38 ; 46B42 ; 46B28 ; Banach function space ; p ; th power ; compact operator ; homogeneous operator
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：12
• 期：1
• 页码：89-115
• 全文大小：397 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper, we characterize compact linear operators from Banach function spaces to Banach spaces by means of approximations with bounded homogeneous maps. To do so, we undertake a detailed study of such maps, proving a factorization theorem and paying special attention to the equivalent strong domination property involved. Some applications to compact maximal extensions of operators are also given.