Abstract of a paper by Kallol Paul, Debmalya Sain and Kanhaiya Jha
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 or http://arXiv.org/abs/1211.6489
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