International Journal of Functional Analysis, Operator Theory and Applications
Volume 9, Issue 3, Pages 85 - 95
(October 2017)
http://dx.doi.org/10.17654/FA009030085 |
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SUPPORTING VECTORS OF CONTINUOUS LINEAR PROJECTIONS
Francisco Javier GarcÃa-Pacheco and Enrique Naranjo-Guerra
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Abstract:
This paper is aimed at studying the supporting vectors of continuous linear projections on Banach spaces, that is, the unit vectors at which a projection attains its norm. We first characterize supporting vectors of general continuous linear operators between Banach spaces. Then we characterize M-projections in terms of supporting vectors. Finally, by means of the supporting vectors again, we provide a characterization of projections of norm 1 on strictly convex Banach spaces. |
| Keywords and phrases: projection, supporting vector. |
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