Displaying similar documents to “Some inequalities of the Grüss type for the numerical radius of bounded linear operators in Hilbert spaces.”

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. ...

Numerical radius inequalities for Hilbert space operators. II

Mohammad El-Haddad, Fuad Kittaneh (2007)

Studia Mathematica

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We give several sharp inequalities involving powers of the numerical radii and the usual operator norms of Hilbert space operators. These inequalities, which are based on some classical convexity inequalities for nonnegative real numbers and some operator inequalities, generalize earlier numerical radius inequalities.

Numerical radius inequalities for 2 × 2 operator matrices

Omar Hirzallah, Fuad Kittaneh, Khalid Shebrawi (2012)

Studia Mathematica

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We derive several numerical radius inequalities for 2 × 2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.

Improved Heinz inequalities via the Jensen functional

Mario Krnić, Josip Pečarić (2013)

Open Mathematics

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By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.