Journal article
Norm and numerical radius of single operators through tools and techniques from multivariable operator theory
Linear algebra and its applications, Vol.649, pp.301-325
09/15/2022
DOI: 10.1016/j.laa.2022.05.009
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⁎–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.
Details
- Title: Subtitle
- Norm and numerical radius of single operators through tools and techniques from multivariable operator theory
- Creators
- Raúl E. Curto - University of IowaSang Hoon Lee - Chungnam National UniversityJasang Yoon - The University of Texas Rio Grande Valley
- Resource Type
- Journal article
- Publication Details
- Linear algebra and its applications, Vol.649, pp.301-325
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.laa.2022.05.009
- ISSN
- 0024-3795
- eISSN
- 1873-1856
- Grant note
- DOI: 10.13039/100007130, name: University of Texas System; DOI: 10.13039/501100003141, name: Consejo Nacional de Ciencia y Tecnología; DOI: 10.13039/501100003725, name: National Research Foundation of Korea, award: 2020R1A2C1A0100584612
- Language
- English
- Date published
- 09/15/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984262748402771
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