Inverse continuity on the boundary of the numerical range

Timothy Leake, Brian Lins, Ilya M. Spitkovsky

Research output: Contribution to journalArticle

Abstract

Let (Formula presented.). We consider the mapping (Formula presented.) , defined on the unit sphere in (Formula presented.). The map has a multi-valued inverse (Formula presented.) , and the continuity properties of (Formula presented.) are considered in terms of the structure of the set of pre-images for points in the numerical range. It is shown that there may be only finitely many failures of continuity of (Formula presented.) , and conditions for where these failure occur are given. Additionally, we give a necessary and sufficient condition for weak inverse continuity to hold for (Formula presented.) and a sufficient condition for (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1335-1345
Number of pages11
JournalLinear and Multilinear Algebra
Volume62
Issue number10
DOIs
StatePublished - Oct 1 2014

Keywords

  • Field of values
  • inverse continuity
  • numerical range
  • weak continuity

ASJC Scopus subject areas

  • Algebra and Number Theory

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