Journal article
COMPLETE SPECTRAL SETS AND NUMERICAL RANGE
Proceedings of the American Mathematical Society, v 146(3), pp 1189-1195
01 Mar 2018
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete C- spectral set for an operator T, then it is a complete M- numerical radius set, where M = 1/2 (C + C-1). In particular, in view of Crouzeix's theorem, there is a universal constant M (less than 5.6) so that if P is a matrix polynomial and T is an element of B(H), then w(P(T)) = M <=parallel to P parallel to(W(T)). When W(T) = (D) over bar, we have M = 5/4.
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Details
- Title
- COMPLETE SPECTRAL SETS AND NUMERICAL RANGE
- Creators
- Kenneth R. Davidson - University of WaterlooVern I. Paulsen - University of WaterlooHugo J. Woerdeman - Drexel University
- Publication Details
- Proceedings of the American Mathematical Society, v 146(3), pp 1189-1195
- Publisher
- Amer Mathematical Soc
- Number of pages
- 7
- Grant note
- NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC) Simons Foundation Institute for Quantum Computing at the University of Waterloo
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000423480000027
- Scopus ID
- 2-s2.0-85041539524
- Other Identifier
- 991019168505704721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied