@article { author = {Nabavi Sales, Seyed Mohammad Sadegh}, title = {On Approximate Birkhoff-James Orthogonality and Approximate $\ast$-orthogonality in $C^\ast$-algebras}, journal = {Sahand Communications in Mathematical Analysis}, volume = {13}, number = {1}, pages = {153-163}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.62262.233}, abstract = {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 $\mathcal{A}$, 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.}, keywords = {Approximate orthogonality,Birkhoff--James orthogonality,Range-kernel orthogonality,$C^\ast$-algebra,$\ast$-orthogonality}, url = {https://scma.maragheh.ac.ir/article_30861.html}, eprint = {https://scma.maragheh.ac.ir/article_30861_f0543a2f5639a20e512cc2c244fb4bd2.pdf} }