arXiv:2008.12705 Abstract | arXiv Analytics

arXiv:2008.12705 [math.FA]Abstract References Reviews Resources

On a new norm on $\mathcal{B}({\mathcal{H}})$ and its applications to numerical radius inequalities

Published 2020-08-28Version 1

We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate with examples that our results improve on some of the important existing numerical radius inequalities.

Categories: math.FA

Subjects: 47A30, 47A12, 47A63

Keywords: application, bounded linear operators, complex hilbert space, important existing numerical radius inequalities, usual operator norm

Related articles: Most relevant | Search more

arXiv:0712.1302 [math.FA] (Published 2007-12-10)

Spectrum of the product of Toeplitz matrices with application in probability

Bernard Bercu, Jean-Francois Bony, Vincent Bruneau

arXiv:1507.01431 [math.FA] (Published 2015-07-06)

Estimates on the norm of polynomials and applications

Gustavo Araújo, Pablo Jiménez-Rodríguez, Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda

arXiv:1703.04045 [math.FA] (Published 2017-03-11)

Stechkin's problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applications