On characterizations of inner product spaces
نویسندگان
چکیده
منابع مشابه
$C^{*}$-semi-inner product spaces
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متن کاملOn a Characterisation of Inner Product Spaces
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 pro...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0374873-0