A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
TLDR
In this paper, it was shown that if A is a bounded linear operator on a complex Hilbert space, then w(A) ≤ 2 (A + A 2 1/2 ) where A is the usual operator norm.Abstract:
It is shown that if A is a bounded linear operator on a complex Hilbert space, then w(A) ≤ 2 (‖A‖+ ‖A2‖1/2), where w(A) and ‖A‖ are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.read more
Citations
More filters
Journal ArticleDOI
On upper and lower bounds of the numerical radius and an equality condition
TL;DR: In this paper, an inequality relating the operator norm of T and the numerical radii of T with respect to the Aluthge transform and its Algorithms was given, which is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158].
Journal ArticleDOI
Numerical Radius Inequalities for Certain 2 × 2 Operator Matrices
TL;DR: In this paper, the numerical radius inequalities for certain 2 × 2 operator matrices were shown for bounded linear operators on a Hilbert space, where X, Y, Z, and W are bounded linear matrices.
Book
Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces
TL;DR: In this article, some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given, and some of the elementary inequalities are discussed.
Posted Content
Numerical radius inequalities for Hilbert Space Operators
TL;DR: In this article, an improvement of Holder-McCarty inequality is established and several refinements of the generalized mixed Schwarz inequality are obtained based on that, and some new numerical radius inequalities are proved.
Journal ArticleDOI
Numerical Radius Inequalities for Hilbert Space Operators
TL;DR: In this article, an improvement of the Holder-McCarty inequality is established, based on which several refinements of the generalized mixed Schwarz inequality are obtained, and some new numerical radius inequalities are proved.
References
More filters
Book
Geometry of Polynomials
TL;DR: In the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history.
Journal ArticleDOI
Buzano's inequality and bounds for roots of algebraic equations
Masatoshi Fujii,Fumio Kubo +1 more
TL;DR: In this paper, a new bound for roots of algebraic equations was given as a consequence of an inequality due to Buzano, which is the first bound for algebraic roots.