Numerical radius inequalities for Hilbert space operators
Fuad Kittaneh (2005)
Studia Mathematica
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It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained. ...