University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras1531633086110.22130/scma.2018.62262.233ENSeyed Mohammad Sadegh Nabavi SalesDepartment of Mathematics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.Journal Article20170418We 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 $mathcal{A}$, 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.http://scma.maragheh.ac.ir/article_30861_f0543a2f5639a20e512cc2c244fb4bd2.pdf