SYLVESTER EQUATIONS AND POLYNOMIAL SEPARATION OF SPECTRA

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Abstract

Sylvester equations AX - XB = C have unique solutions for all C when the spectra of A and B are disjoint. Here A and B are bounded operators in Banach spaces. We discuss the existence of polynomials p such that the spectra of p(A) and p(B) are well separated, either inside and outside of a circle or separated into different half planes. Much of the discussion is based on the following inclusion sets for the spectrum: V-p(T) = {lambda is an element of C : vertical bar p(lambda)vertical bar

Details

Original languageEnglish
Pages (from-to)867-885
Number of pages19
JournalOPERATORS AND MATRICES
Volume13
Issue number3
Publication statusPublished - Sep 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Sylvester equation, multicentric calculus, preconditioning, spectral separation

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