Numerical Radius Parallelism of Hilbert Space Operators.

In this paper, we study the numerical radius parallelism for bounded linear operators on a Hilbert space (H , ⟨ · , · ⟩) . More precisely, we consider bounded linear operators T and S which satisfy ω (T + λ S) = ω (T) + ω (S) for some complex unit λ , and is denoted by T ‖ ω S . We show that T ‖ ω S if and only if there exists a sequence of unit vectors { x n } in H such that lim n → ∞ | ⟨ T x n , x n ⟩ ⟨ S x n , x n ⟩ | = ω (T) ω (S). We then apply it to give some applications. [ABSTRACT FROM AUTHOR]