Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774652 | Journal of Mathematical Analysis and Applications | 2018 | 12 Pages |
Abstract
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a nonzero bounded linear operator to attain norm at a particular point of the unit sphere. We prove four corollaries to establish the importance of our study. As part of our exploration, we also obtain a characterization of smooth Banach spaces in terms of operator norm attainment and Birkhoff-James orthogonality. Restricting our attention to lp2(pâNâ{1}) spaces, we obtain an upper bound for the number of points at which any linear operator, which is not a scalar multiple of an isometry, may attain norm.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Debmalya Sain,