Abstract

We study the properties of rectangular constant μ(X)\mu(\mathbb{X}) in a normed linear space X\mathbb{X}. We prove that μ(X)=3\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 X\mathbb{X} is finite then μ(X)\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.

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Keywords

  • Birkhoff-James Orthogonality
  • rectangular constant

Mathematics Subject Classification

46B20; 47A30

References

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Suggested citation

K. Paul, P. Ghosh, D. Sain. “On Rectangular Constant in Normed Linear Spaces.” Journal of Convex Analysis 24 (2017), No. 3, 917–925. https://doi.org/10.68381/jca24054

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.