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Homogeneity of Pythagorean Orthogonality and Related Inequalities(PDF)

《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

Issue:
2013年05期
Page:
115-118
Research Field:
数理科学
Publishing date:

Info

Title:
Homogeneity of Pythagorean Orthogonality and Related Inequalities
Author(s):
WU Sen- lin GUO Wei
School of Applied Sciences,Harbin University of Science and Technology
Keywords:
Birkhoff orthogonality homogeneity of Pythagorean orthogonality Roberts orthogonality
PACS:
O177
DOI:
-
Abstract:
Abstract: We study the homogeneity of Pythagorean orthogonality in normed linear spaces. It is proved that
Pythagorean orthogonality is unique at x if x is a homogeneous direction of Pythagorean orthogonality. At the same
time,we study the ralation between homogeneous direction of Pythagorean orthogonality and other notions including
isometric reflection vectors and L2 - summand vectors,and show that a Banach space X is a Hilbert space if and only
if the relative interior of the set of homogeneous dierections of Pythagorean orthogonality in the unit sphere of X is
not empty. We introduce a geometric constant NPX to measure the non- homogeneity of Pythagorean orthogonality. It
is proved that NPX = 0 if and only if X is a Hilbert space.

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Last Update: 2013-12-26