Open AccessSome characterizations of strongly partial isometry elements in rings with involutions
Author(s) -
Shiyin Zhao,
Junchao Wei
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2203843z
Subject(s) - mathematics , isometry (riemannian geometry) , invertible matrix , constructive , element (criminal law) , pure mathematics , set (abstract data type) , combinatorics , law , process (computing) , computer science , political science , programming language , operating system
In this paper, we study an element which is both group invertible and Moore Penrose invertible to be EP, partial isometry and strongly EP by discussing the existence of solutions in a definite set of some given constructive equations. Mainly, let a ? R# ? R+. Then we firstly show that an element a ? REP if and only if and Equation : axa+ + a+ax = 2x has at least one solution in ?a = {a, a#, a+, a+, (a#)+, (a+)+}. Next, a ? RSEP if and only if Equation: axa+ + a+ax = 2x has at least one solution in ?a. Finally, a ? RPI if and only if Equation: aya+x = xy has at least one solution in ?2a , where ?a = {a, a#, a+, (a#)+, (a+)+}.