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

Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when thespectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators inBanach spaces. We discuss the existence of polynomials $p$ such that thespectra of $p(A)$ and $p(B)$ are well separated, either inside and outside of acircle or separated into different half planes. Much of the discussion is basedon the following inclusion sets for the spectrum: $V_p(T)=\{\lambda \in \mathbbC \ : \ |p(\lambda)| \le \|p(T)\| \}$ where $T$ is a bounded operator. We alsogive an explicit series expansion for the solution in terms of $p(M)$, where$M=\begin{pmatrix} A&C\\ &B\end{pmatrix}$, in the case where the spectra of $A$and $B$ lie in different components of $V_p(M)$ .

Sylvester equations and polynomial separation of spectra