2020/03/31 by Feki, Kais
#46C05 #47A12 #47A30 #47A63 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2003.14378
Let A be a positive (semidefinite) bounded linear operator acting on a complex Hilbert space (H, ⟨ ⋅| ⋅⟩ ). The semi-inner product ⟨ x| y⟩A := ⟨ Ax| y⟩, x, y\inH induces a seminorm ‖⋅‖A on H. Let T be an A-bounded operator on H, the A-numerical radius of T is given by ωA(T) = sup\|⟨ Tx| x⟩A|: x∈ H, ‖x‖A = 1\. In this paper, we establish several inequalities for ω_\mathbbA(\mathbbT), where \mathbbT=(Tij) is a d× d operator matrix with Tij are A-bounded operators and \mathbbA is the diagonal operator matrix whose each diagonal entry is A.