2024/07/31 by Guesba, Messaoud, Barik, Somdatta, Bhunia, Pintu +1
#47A05 #47A12 #47A30 #47B15 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2407.21639
Consider H is a complex Hilbert space and A is a positive operator on H. The mapping ⟨⋅,⋅⟩A: H× H → \mathbb C, defined as ⟨ y,z⟩A=⟨ Ay,z⟩ for all y,z ∈ H, induces a seminorm \Vert ⋅\VertA. The A-Davis-Wielandt radius of an operator S on H is defined as dωA( S) =sup \ √\vert ⟨ Sz,z⟩A\vert 2+\Vert Sz\VertA4 :\Vert z\VertA=1\ . We investigate some new bounds for dωA( S) which refine the existing bounds. We also give some bounds for the 2× 2 off-diagonal block matrices.