# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Numerical radius inequalities for Hilbert space operators

### Tom 168 / 2005

Studia Mathematica 168 (2005), 73-80 MSC: 47A12, 47A30, 47A63, 47B47. DOI: 10.4064/sm168-1-5

#### Streszczenie

It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $${1 \over 4}\| {A^* A + AA^* } \| \le ( {w(A )} )^2 \le {1 \over 2}\| {A^* A + AA^* }\| ,$$ where $w(\cdot )$ and $\| \cdot \|$ are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities $${1 \over 2}\| A \| \le w( A ) \le \| A \| .$$ Numerical radius inequalities for products and commutators of operators are also obtained.