Abstract:We study the properties of rectangular constant µ(X) in a normed linear space X. We prove that µ(X) = 3 iff the unit sphere contains a straight line segment of length 2. In fact, we prove that the rectangular modulus attains its upper bound iff the unit sphere contains a straight line segment of length 2. We prove that if the dimension of the space X is finite then µ(X) is attained. We also prove that a normed linear space is an inner product space iff we have sup{ 1+|t|2010 Mathematics Subject Classification.… Show more
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