scholarly journals Circle-Uniqueness of Pythagorean Orthogonality in Normed Linear Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Senlin Wu ◽  
Xinjian Dong ◽  
Dan Wang
Keyword(s):  
Unit Sphere ◽  
Linear Spaces ◽  
Strictly Convex ◽  
Normed Linear Spaces ◽  
Underlying Space ◽  
Pythagorean Orthogonality

We introduce the circle-uniqueness of Pythagorean orthogonality in normed linear spaces and show that Pythagorean orthogonality is circle-unique if and only if the underlying space is strictly convex. Further related results providing more detailed relations between circle-uniqueness of Pythagorean orthogonality and the shape of the unit sphere are also presented.

scholarly journals Orthogonality and characterizations of inner product spaces

1978 ◽  
Vol 19 (3) ◽  
pp. 403-416 ◽  
Author(s):  
O.P. Kapoor ◽  
Jagadish Prasad
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Inner Product ◽  
Product Spaces ◽  
Isosceles Orthogonality ◽  
Linear Spaces ◽  
Strictly Convex ◽  
Inner Product Spaces ◽  
James Orthogonality ◽  
Pythagorean Orthogonality

Using the notions of orthogonality in normed linear spaces such as isosceles, pythagorean, and Birkhoff-James orthogonality, in this paper we provide some new characterizations of inner product spaces besides giving simpler proofs of existing similar characterizations. In addition we prove that in a normed linear space pythagorean orthogonality is unique and that isosceles orthogonality is unique if and only if the space is strictly convex.

An orthogonality in normed linear spaces based on angular distance inequality

2015 ◽  
Vol 90 (2) ◽  
pp. 281-297 ◽  
Author(s):  
F. Dadipour ◽  
F. Sadeghi ◽  
A. Salemi
Keyword(s):  
Angular Distance ◽  
Linear Spaces ◽  
Normed Linear Spaces
Sign in / Sign up

Export Citation Format

Share Document