Norm and numerical radius of single operators through tools and techniques from multivariable operator theory

Authors

Raul E. Curto, University of Iowa
Sang Hoon Lee
Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-15-2022

Abstract

We employ tools and techniques from multivariable operator theory to obtain new proofs and extensions of well known inequalities regarding the norm and the numerical radius of elementary operators defined on the C⁎" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">C⁎C⁎–algebra of all bounded operators on Hilbert space, or on the ⁎–ideal of Hilbert-Schmidt operators. In the process, we provide new insights on the study of Heinz-type inequalities related to the arithmetic-geometric mean inequality, and generalize results of several authors, including R. Bhatia, G. Corach, C. Davis, F. Kittaneh, and M.S. Moslehian. To estimate the norm, our approach exploits, in particular, the Spectral Mapping Theorem for the Taylor spectrum, and Ky Fan's Dominance Theorem. For the numerical radius, we use S. Hildebrandt's description of the numerical range of an operator in terms of the norm of its translates.

Comments

Original published version available at https://doi.org/10.1016/j.laa.2022.05.009

Recommended Citation

Curto, Raúl E., Sang Hoon Lee, and Jasang Yoon. "Norm and numerical radius of single operators through tools and techniques from multivariable operator theory." Linear Algebra and its Applications 649 (2022): 301-325. https://doi.org/10.1016/j.laa.2022.05.009

Publication Title

Linear Algebra and its Applications

DOI

10.1016/j.laa.2022.05.009