Furtherance of Numerical radius inequalities of Hilbert space operators

Abstract

If $A,B$ are bounded linear operators on a complex Hilbert space, then % $w(A)\le \frac{1}{2}\left(\Vert A\Vert +\sqrt{r\left(|A||A^{\ast }|\right)}\right)$ and $w(AB\pm BA)\le 2\sqrt{2}\Vert B\Vert \sqrt{w^2(A)-\frac{c^2(\Re (A))+c^2(\Im (A))}{2}},$ \begin{eqnarray*} w(A) &\leq& \frac{1}{2}\left( \|A\|+\sqrt{r\left(|A||A^*|\right)}\right),\\ w(AB \pm BA)&\leq& 2\sqrt{2}\|B\|\sqrt{ w^2(A)-\frac{c^2(\Re (A))+c^2(\Im (A))}{2} }, \end{eqnarray*} where $w(.),\Vert .\Vert ,c(.)$ and $r(.)$ are the numerical radius, the operator norm, the Crawford number and the spectral radius respectively, and $\Re (A)$, $\Im (A)$ are the real part, the imaginary part of $A$ respectively. The inequalities obtained here generalize and improve on the existing well known inequalities.

9 pages

References in corpus (1)

• Proper improvement of well-known numerical radius inequalities and their applications

Cited by in corpus (8)

• Euclidean operator radius inequalities of a pair of bounded linear operators and their applications
• Numerical radius inequalities of $2\times 2$ operator matrices
• Numerical radius inequalities for tensor product of operators
• Numerical radius inequalities and estimation of zeros of polynomials
• Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
• Refined inequalities for the numerical radius of Hilbert space operators
• Numerical radius inequalities of sectorial matrices
• Improvement of numerical radius inequalities