On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras - Seyed Mohammad Sadegh Nabavi Sales (Sahand Communications in Mathematical Analysis, 2019)
We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary $C^ast$-algebra $mathcalA$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.