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A Reverse Theorem on the ·-w* Continuity of the Dual Map
Joint Authors
Garcia-Pacheco, F. J.
de Kock, Mienie
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-10
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
Given a Banach space X, x∈?X, and ?Xx=x*∈?X*:x*x=1, we define the set ?X*x of all x*∈?X* for which there exist two sequences xnn∈N⊆?X∖{x} and xn*n∈N⊆?X* such that xnn∈N converges to x, xn*n∈N has a subnet w*-convergent to x*, and xn*xn=1 for all n∈N.
We prove that if X is separable and reflexive and X* enjoys the Radon-Riesz property, then ?X*x is contained in the boundary of ?Xx relative to ?X*.
We also show that if X is infinite dimensional and separable, then there exists an equivalent norm on X such that the interior of ?Xx relative to ?X* is contained in ?X*x.
American Psychological Association (APA)
de Kock, Mienie& Garcia-Pacheco, F. J.. 2015. A Reverse Theorem on the ·-w* Continuity of the Dual Map. Journal of Function Spaces،Vol. 2015, no. 2015, pp.1-4.
https://search.emarefa.net/detail/BIM-1068332
Modern Language Association (MLA)
de Kock, Mienie& Garcia-Pacheco, F. J.. A Reverse Theorem on the ·-w* Continuity of the Dual Map. Journal of Function Spaces No. 2015 (2015), pp.1-4.
https://search.emarefa.net/detail/BIM-1068332
American Medical Association (AMA)
de Kock, Mienie& Garcia-Pacheco, F. J.. A Reverse Theorem on the ·-w* Continuity of the Dual Map. Journal of Function Spaces. 2015. Vol. 2015, no. 2015, pp.1-4.
https://search.emarefa.net/detail/BIM-1068332
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068332