Orthogonal Symmetries and Reflections in Banach Spaces
Joint Authors
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-06-14
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Let X be a Banach space.
We introduce a concept of orthogonal symmetry and reflection in X.
We then establish its relation with the concept of best approximation and investigate its implication on the shape of the unit ball of the Banach space X by considering sections over subspaces.
The results are then applied to the space C(I) of continuous functions on a compact set I.
We obtain some nontrivial symmetries of the unit ball of C(I).
We also show that, under natural symmetry conditions, every odd function is orthogonal to every even function in X.
We conclude with some suggestions for further investigations.
American Psychological Association (APA)
Jaballah, Ali& Saidi, Fathi B.. 2017. Orthogonal Symmetries and Reflections in Banach Spaces. Journal of Mathematics،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1182339
Modern Language Association (MLA)
Jaballah, Ali& Saidi, Fathi B.. Orthogonal Symmetries and Reflections in Banach Spaces. Journal of Mathematics No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1182339
American Medical Association (AMA)
Jaballah, Ali& Saidi, Fathi B.. Orthogonal Symmetries and Reflections in Banach Spaces. Journal of Mathematics. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1182339
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1182339