Numerical radius inequalities involving commutators of G₁ operators

الأصل · EN

We prove numerical radius inequalities involving commutators of G₁ operators and certain analytic functions. Among other inequalities, it is shown that if A and X are bounded linear operators on a complex Hilbert space, then equation* w(f(A)X+Xf(A))≤ 2dₐ²w(X-AXA), equation* where A is a G₁ operator with σ(A)⊂ D and f is analytic on the unit disk D such that Re(f)>0 and f(0)=1.