Numerical Radius Parallelism of Hilbert Space Operators

Abstract

In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space H , ·, · based on numerical radius. More precisely, we consider operators T and S which satisfy ω(T + λS) = ω(T ) + ω(S) for some complex unit λ. We show that T ω S if and only if there exists a sequence of unit vectors {xn} in H such that lim n→∞ T xn, xn Sxn, xn = ω(T )ω(S).We then apply it to give some applications. z, y x for all z ∈ H . Also, we shall use [x] to denote the linear space spanned by vector x ∈ H .

A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications

“…In addition, a characterization of the A-numerical radius parallelism of A-rank one operators is established. Our results cover and extend the works in [16,18]. In the last section, we give some inequalities for A-numerical radius of semi-Hilbertian space operators which are as an application of A-numerical radius orthogonality and parallelism.…”

Davis–Wielandt shells of semi-Hilbertian space operators and its applications

“…Recently, a new type of parallelism for Hilbert space operators based on numerical radius has been introduced by M. Mehrazin et al in [20] as follows. The following result gives a characterization of the numerical radius parallelism for Hilbert space operators.…”

“…Recently, a new type of parallelism for Hilbert space operators based on numerical radius has been introduced by M. Mehrazin et al in [20] as follows.…”

“…The following result gives a characterization of the numerical radius parallelism for Hilbert space operators. The proof can be found in [20,Theorem 2.2] Theorem 1.4. ([20, Theorem 2.2]) Let T, S ∈ B(H).…”