This is an announcement for the paper "On strong orthogonality and strictly convex normed linear spaces" by Kallol Paul, Debmalya Sain and Kanhaiya Jha.
Abstract: We introduce the notion of strongly orthogonal set relative to an element in the sense of Birkhoff-James in a normed linear space to find a necessary and sufficient condition for an element $ x $ of the unit sphere $ S_{X}$ to be an exposed point of the unit ball $ B_X .$ We then prove that a normed linear space is strictly convex iff for each element x of the unit sphere there exists a bounded linear operator A on X which attains its norm only at the points of the form $ \lambda x $ with $ \lambda \in S_{K} $.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 47A30
Submitted from: kalloldada@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.6489
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