Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom