On a Characterisation of Inner Product Spaces

Autor:	G. Z. Chelidze
Rok vydání:	2001
Předmět:	Strictly convex space Discrete mathematics Combinatorics Inner product space Energetic space Polarization identity General Mathematics Cylinder set measure Dual norm Reproducing kernel Hilbert space Mathematics Normed vector space
Zdroj:	gmj. 8:231-236
ISSN:	1572-9176 1072-947X
DOI:	10.1515/gmj.2001.231
Popis:	It is well known that for the Hilbert space H the minimum value of the functional F μ (f) = ∫ H ‖f – g‖2 dμ(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.
Databáze:	OpenAIRE
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