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Let \(\mathcal {H}\) be a complex Hilbert space and let A positive operator on {H}\). We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian {B}_A(\mathcal {H})\) that generalize improve existing ones. Further, we estimate an upper bound \(\mathbb {A}\)-operator seminorm \(2\times 2\) matrices, where {A}=\text{ diag }(A,A)\). The obtained here generalizes earlier relate...

We introduce a new norm on the space of all bounded linear operators complex Hilbert space, which generalizes numerical radius norm, usual operator and modified Davis–Wielandt norm. study basic properties this including upper lower bounds for it. As an application present study, we estimate operators. illustrate that our results improve some important existing inequalities. Other have also stud...

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, import...