English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We define the complete numerical radius norm for homomorphisms from anyoperator algebra into ${\mathcal B}({\mathcal H})$, and show that this norm canbe computed explicitly in terms of the completely bounded norm. This is used toshow that if $K$ is a complete $C$-spectral set for an operator $T$, then it isa complete $M$-numerical radius set, where $M=\frac12(C+C^{-1})$. Inparticular, 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 $T \in {\mathcalB}({\mathcal H})$, then $w(P(T)) \le M \|P\|_{W(T)}$. When $W(T) =\overline{\mathbb D}$, we have $M = \frac54$.

Complete spectral sets and numerical range