Approximate Roberts orthogonality sets and $${(\delta, \varepsilon)}$$ ( δ , ε ) -(a, b)-isosceles-orthogonality preserving mappings

2015 ◽  
Vol 90 (3) ◽  
pp. 647-659 ◽  
Author(s):  
Ali Zamani ◽  
Mohammad Sal Moslehian
Keyword(s):  
Isosceles Orthogonality ◽  
Roberts Orthogonality

scholarly journals A Remark on the Homogeneity of Isosceles Orthogonality

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Chan He ◽  
Dan Wang
Keyword(s):  
Isosceles Orthogonality ◽  
Inner Products ◽  
Definition Of ◽  
Homogeneity Of Isosceles Orthogonality

Inspired by the definition of homogeneous direction of isosceles orthogonality, we introduce the notion of almost homogeneous direction of isosceles orthogonality and show that, surprisingly, these two notions coincide. Several known characterizations of inner products are improved.

Isosceles-orthogonality preserving property and its stability

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1445-1453 ◽  
Author(s):  
Jacek Chmieliński ◽  
Paweł Wójcik
Keyword(s):  
Isosceles Orthogonality

scholarly journals On Carlsson type orthogonality and characterization of inner product spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 859-870 ◽  
Author(s):  
Eder Kikianty ◽  
Sever Dragomir
Keyword(s):  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Isosceles Orthogonality ◽  
Inner Product Spaces ◽  
Pythagorean Orthogonality

In an inner product space, two vectors are orthogonal if their inner product is zero. In a normed space, numerous notions of orthogonality have been introduced via equivalent propositions to the usual orthogonality, e.g. orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of a normed space. Some notions of orthogonality have been introduced by utilizing the 2-HH-norm [10]. These notions of orthogonality are closely related to the classical Pythagorean orthogonality and Isosceles orthogonality. In this paper, a Carlsson type orthogonality in terms of the 2-HH-norm is considered, which generalizes the previous definitions. The main properties of this orthogonality are studied and some useful consequences are obtained. These consequences include characterizations of inner product space.

scholarly journals On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Bhuwan Prasad Ojha ◽  
Prakash Muni Bajracharya ◽  
Vishnu Narayan Mishra
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Inner Product ◽  
Isosceles Orthogonality ◽  
Complete Proof ◽  
Underlying Space ◽  
Real Inner Product Space ◽  
Special Case ◽  
Real Normed Linear Space ◽  
Pythagorean Orthogonality

This paper generalizes the special case of the Carlsson orthogonality in terms of the 2-HH norm in real normed linear space. Dragomir and Kikianty (2010) proved in their paper that the Pythagorean orthogonality is unique in any normed linear space, and isosceles orthogonality is unique if and only if the space is strictly convex. This paper deals with the complete proof of the uniqueness of the new orthogonality through the medium of the 2-HH norm. We also proved that the Birkhoff and Robert orthogonality via the 2-HH norm are equivalent, whenever the underlying space is a real inner-product space.

scholarly journals On Birkhoff – James and Roberts orthogonality

2018 ◽  
Vol 6 (1) ◽  
pp. 229-236 ◽  
Author(s):  
Ljiljana Arambašic ◽  
Rajna Rajic
Keyword(s):  
C Algebras ◽  
Roberts Orthogonality

Abstract In this paper we present some recent results on characterizations of the Birkhoff-James and the Roberts orthogonality in C*-algebras and Hilbert C*-modules.

Approximate Roberts orthogonality

2013 ◽  
Vol 89 (3) ◽  
pp. 529-541 ◽  
Author(s):  
Ali Zamani ◽  
Mohammad Sal Moslehian
Keyword(s):  
Roberts Orthogonality
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