On a Characterisation of Inner Product Spaces
نویسنده
چکیده
It is well known that for the Hilbert space H the minimum value of the functional Fμ(f) = ∫ H ‖f−g‖2dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner product that generates the norm. 2000 Mathematics Subject Classification: 46C15.
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