Norm Attaining Multilinear Forms on L1(μ)
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-06-16
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Given an arbitrary measure μ, this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on L1(μ).
However, we have the density if and only if μ is purely atomic.
Furthermore, the study presents an example of a Banach space X in which the set of norm attaining operators from X into X∗ is dense in the space of all bounded linear operators L(X,X∗).
In contrast, the set of norm attaining bilinear forms on X is not dense in the space of continuous bilinear forms on X.
American Psychological Association (APA)
Saleh, Yousef. 2008. Norm Attaining Multilinear Forms on L1(μ). International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-6.
https://search.emarefa.net/detail/BIM-987885
Modern Language Association (MLA)
Saleh, Yousef. Norm Attaining Multilinear Forms on L1(μ). International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-6.
https://search.emarefa.net/detail/BIM-987885
American Medical Association (AMA)
Saleh, Yousef. Norm Attaining Multilinear Forms on L1(μ). International Journal of Mathematics and Mathematical Sciences. 2008. Vol. 2008, no. 2008, pp.1-6.
https://search.emarefa.net/detail/BIM-987885
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987885