Inverse continuity of the numerical range map for hilbert space operators

Brian Lins, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


We describe continuity properties of the multivalued inverse of the numerical range map fA: x →(Ax,x) associated with a linear operator A defined on a complex Hilbert space H. We prove in particular that f-1 A is strongly continuous at all points of the interior of the numerical range W(A). We give examples where strong and weak continuity fail on the boundary and address special cases such as normal and compact operators.

Original languageEnglish (US)
Article numberOaM-14-06
Pages (from-to)77-90
Number of pages14
JournalOperators and Matrices
Issue number1
StatePublished - Mar 2020


  • Inverse continuity
  • Numerical range
  • Weak continuity

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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