فهرست نشریات علمی دسترسی آزاد ایران

‎Assume that $ \mathcal{A} $ is a unital C*-algebra and $ a\in\mathcal{A} $ is a positive and invertible element‎. ‎Set \[ \mathcal{S}_a (\mathcal{A})=\{ \dfrac{f}{f(a)} \‎, : ‎\‎, ‎f \in \mathcal{S}(\mathcal{A})‎, ‎\‎, ‎f(a)\neq 0\}‎, ‎\] where $ \mathcal{S}(\mathcal{A}) $ is the state space of $ \mathcal{A} $‎. ‎The main aim of this paper is to introduce and study the notions of approximate a-orthogonality and approximate a-Birkhoff-James orthogonality associated to the norm‎: ‎\[ \|x\|_a = \sup_{\varphi \in \mathcal{S}_a(\mathcal{A})} \sqrt{\varphi(x* ax)}\quad (x\in \mathcal{A}),\] in C*-algebra $\mathcal{A}$‎.‎First‎, ‎by providing some examples‎, ‎we show that these approximate orthogonalities are generally incomparable in non-commutative C*-algebras‎. ‎Next‎, ‎we will see that under what conditions‎, ‎these orthogonality relationships are related‎. ‎Also‎, ‎two different characterizations of approximate a-Birkhoff-James orthogonality in terms of the elements of $ \mathcal{S}_a (\mathcal{A}) $ are obtained‎.‎Moreover‎, ‎the strong version of approximate a-Birkhoff-James orthogonality is studied‎. ‎Finally‎, ‎we prove that if approximate a-Birkhoff-James orthogonality and its strong version coincide on $ \mathcal{A} $‎, ‎then $ \mathcal{A} $ is commutative‎.