Anderson's theorem for compact operators

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

It is shown that if A is a compact operator on a Hilbert space with its numerical range W(A) contained in the closed unit disc double-struck D sign̄ and with W(A) intersecting the unit circle at infinitely many points, then W(A) is equal to double-struck D sign̄. This is an infinite-dimensional analogue of a result of Anderson for finite matrices.

Original languageEnglish
Pages (from-to)3159-3162
Number of pages4
JournalProceedings of the American Mathematical Society
Volume134
Issue number11
DOIs
StatePublished - Nov 2006

Keywords

  • Compact operator
  • Numerical range

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