Consider H is a complex Hilbert space and A is a positive operator on H. The mapping ·,·A: H× H → C, defined as y,zA= Ay,z for all $y,z$ ∈ H, induces a seminorm ·A. The A-Davis-Wielandt radius of an operator S on H is defined as dωA( S) = \ √ Sz,zA ²+ SzA⁴ : zA=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.
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Guesba et al. (2024) studied this question.
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