Displaying similar documents to “On the joint numerical status and tensor products.”

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

Antonio J. Guirao, Olena Kozhushkina (2013)

Studia Mathematica

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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).

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

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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.

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. ...

A convex treatment of numerical radius inequalities

Zahra Heydarbeygi, Mohammad Sababheh, Hamid Moradi (2022)

Czechoslovak Mathematical Journal

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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

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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.