Orthogonal Symmetries and Reflections in Banach Spaces

Autor: Ali Jaballah, Fathi B. Saidi
Jazyk: angličtina
Rok vydání: 2017
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Zdroj: Journal of Mathematics, Vol 2017 (2017)
Druh dokumentu: article
ISSN: 2314-4629
2314-4785
DOI: 10.1155/2017/1073589
Popis: 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.
Databáze: Directory of Open Access Journals
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