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Middle points and inner products
Author(s) -
Benítez Carlos,
Yáñez Diego
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm068
Subject(s) - mathematics , chord (peer to peer) , inner product space , space (punctuation) , point (geometry) , unit sphere , product (mathematics) , combinatorics , unit (ring theory) , pure mathematics , geometry , mathematics education , computer science , distributed computing , operating system
Let X be a real normed space with unit sphere S . It is proved that X is an inner product space if and only if there is a real number ρ , 0 < ρ < 1, and ρ ≠ ( 1 + cos ( 2 k π / n ) ) / 2 ( 2 k < n ; n = 3 , 4 , … ) , such that every chord of S that supports ρS touches ρS at its middle point.