This is an announcement for the paper “On the norm attainment set of a bounded linear operator” by Debmalya Sainhttp://arxiv.org/find/math/1/au:+Sain_D/0/1/0/all/0/1.

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 bounded linear operator attaining norm at a particular point of the unit sphere. We prove a number of 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 $\ell_p^2 (p\in N, p\geq 2)$ 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.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1608.00755