Open AccessProperties of Chmielinski-orthogonality using Kadets-Klee property
Author(s) -
Saied A. Johnny,
Buthainah A. A. Ahmed
Publication year - 2022
Publication title -
iraqi journal for computer science and mathematics
Language(s) - English
Resource type - Journals
eISSN - 2958-0544
pISSN - 2788-7421
DOI - 10.52866/ijcsm.2022.01.01.010
Subject(s) - mathematics , orthogonality , approximation property , banach space , pure mathematics , bounded operator , bounded function , reflexive space , operator (biology) , finite rank operator , pseudo monotone operator , compact operator , space (punctuation) , regular polygon , operator space , mathematical analysis , interpolation space , functional analysis , computer science , geometry , biochemistry , chemistry , repressor , transcription factor , extension (predicate logic) , gene , programming language , operating system
The aim of this paper is to study new results of an approximate orthogonality of Birkhoff-James techniques in real Banach space , namely Chiemelinski orthogonality (even there is no ambiguity between the concepts symbolized by orthogonality) and provide some new geometric characterizations which is considered as the basis of our main definitions. Also, we explore relation between two different types of orthogonalities. First of them orthogonality in a real Banach space and the other orthogonality in the space of bounded linear operator . We obtain a complete characterizations of these two orthogonalities in some types of Banach spaces such as strictly convex space, smooth space and reflexive space. The study is designed to give different results about the concept symmetry of Chmielinski-orthogonality for a compact linear operator on a reflexive, strictly convex Banach space having Kadets-Klee property by exploring a new type of a generalized some results with Birkhoff James orthogonality in the space of bounded linear operators. We also exhibit a smooth compact linear operator with a spectral value that is defined on a reflexive, strictly convex Banach space having Kadets-Klee property either having zero nullity or not -right-symmetric.