Numerical radius inequalities for Hilbert space operators

• Autorzy: Fuad Kittaneh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47A63: Operator inequalities
• 47A12: Numerical range, numerical radius
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 1
• Strony: 73-80

Daty

wydano

2005

Twórcy

autor

Fuad Kittaneh

• Department of Mathematics, University of Jordan, Amman, Jordan

Identyfikatory

DOI

10.4064/sm168-1-5