Narrow Results

The primary objective of this study is to unveil new upper bounds for the numerical radius of operators in Hilbert spaces, utilizing an enhanced version of the McCarthy inequality. These newly derived estimates refine existing inequalities for bounded linear operators.

We apply spectral radius and norm inequalities to certain $2\times 2$ operator matrices to give simple proofs, refinements and generalizations of known norm inequalities. New norm inequalities are also given. Our analysis uncovers the interplay between different spectral radius and norm inequalities.

Finding new bounds for norms and the numerical radius of certain matrix forms is a renowned topic that has attracted numerous researchers. In this paper, we show some new bounds for unitarily invariant norms and the numerical radius of certain matrix forms that involve products of matrices and sums of products.

New arithmetic-geometric mean-type inequalities and a refinement of the celebrated Cauchy–Schwarz inequality are shown among the obtained results.

Our results are compared with those in the literature through numerical examples and rigorous approaches.

Some refinements of the continuous triangle inequality for the Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for norm and numerical radius operator inequalities are provided. A particular case of interest for complex-valued functions is pointed out as well.

In this paper, we present a refinement of the well-known arithmetic-geometric mean inequality. As application of our result, we obtain an operator inequality. We give an improvement of the inequality presented by Kittaneh for the numerical radius.

Several upper estimates for the numerical radius of Hilbert space operators are given. Among many other inequalities, it is shown that if $A,B\in \mathcal{ℬ}(\mathcal{\mathscr{H}})$, then

New numerical radius inequalities for Hilbert space operators are given. We give an improvement of the inequality presented by Kittaneh for numerical radius, in fact we show that if $A\in {ℬ}({\mathscr{H}}),$ then