
Journal of Convex Analysis 24 (2017), No. 3, 917925 Copyright Heldermann Verlag 2017 On Rectangular Constant in Normed Linear Spaces Kallol Paul Dept. of Mathematics, Jadavpur University, Kolkata 700032, India kalloldada@gmail.com Puja Ghosh Dept. of Mathematics, Jadavpur University, Kolkata 700032, India ghosh.puja1988@gmail.com Debmalya Sain Dept. of Mathematics, Jadavpur University, Kolkata 700032, India saindebmalya@gmail.com [Abstractpdf] We study the properties of rectangular constant $\mu(\mathbb{X})$ in a normed linear space $\mathbb{X}$. We prove that $\mu(\mathbb{X}) = 3$ if and only if the unit sphere contains a straight line segment of length 2. In fact, we prove that the rectangular modulus attains its upper bound if and only if the unit sphere contains a straight line segment of length 2. We prove that if the dimension of the space $\mathbb{X}$ is finite then $\mu(\mathbb{X})$ is attained. We also find a necessary and sufficient condition for a normed linear space to be an inner product space in terms of conditions involving rectangular constant. Keywords: BirkhoffJames Orthogonality, rectangular constant. MSC: 46B20; 47A30 [ Fulltextpdf (109 KB)] for subscribers only. 