Displaying similar documents to “Numerical radius inequalities for 2 × 2 operator matrices”

Numerical radius inequalities for Hilbert space operators

Fuad Kittaneh (2005)

Studia Mathematica

Similarity:

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

Similarity:

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 index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

Similarity:

We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

On numerical range of sp(2n, C)

Wen Yan, Jicheng Tao, Zhao Lu (2016)

Special Matrices

Similarity:

In this paper we studied the classical numerical range of matrices in sp(2n, C). We obtained some result on the relationship between the numerical range of a matrix in and that [...] of its diagonal block, the singular values of its off-diagonal block A2.

A convex treatment of numerical radius inequalities

Zahra Heydarbeygi, Mohammad Sababheh, Hamid Moradi (2022)

Czechoslovak Mathematical Journal

Similarity:

We prove an inner product inequality for Hilbert space operators. This inequality will be utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to...

On upper and lower bounds of the numerical radius and an equality condition

Takeaki Yamazaki (2007)

Studia Mathematica

Similarity:

We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.

The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)

Antonio J. Guirao, Olena Kozhushkina (2013)

Studia Mathematica

Similarity:

We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).