scholarly journals Bounds for the p-Angular Distance and Characterizations of Inner Product Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Mario Krnić ◽  
Nicuşor Minculete
Keyword(s):  
Angular Distance ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

scholarly journals Operator inequalities related to p-angular distances

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2107-2111
Author(s):  
Taba Afkhami ◽  
Hossein Dehghan
Keyword(s):  
Normed Space ◽  
Angular Distance ◽  
Inner Product ◽  
Product Spaces ◽  
Operator Inequalities ◽  
Inner Product Spaces ◽  
Operator Version

For any nonzero elements x,y in a normed space X, the angular and skew-angular distance is respectively defined by ?[x,y] = ||x/||x|| - y/||y|||| and ?[x,y] = ||x/||y|| - y/||x||||. Also inequality ? ? ? characterizes inner product spaces. Operator version of ? p has been studied by Pecaric, Rajic, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of p-angular distance ?p by using Douglas? lemma. We also prove that the operator version of inequality ? p ? ?p holds for normal and double commute operators. Some examples are presented to show essentiality of these conditions.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Triangle Congruence Characterizations of Inner Product Spaces

1989 ◽  
Vol 144 (1) ◽  
pp. 81-86
Author(s):  
Charles R. Diminnie ◽  
Edward Z. Andalafte ◽  
Raymond W. Freese
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces
Sign in / Sign up

Export Citation Format

Share Document