A note on Anderson's theorem in the infinite-dimensional setting

Riddhick Birbonshi, Ilya M. Spitkovsky, P. D. Srivastava

Research output: Contribution to journalArticle

Abstract

Anderson's theorem states that if the numerical range W(A) of an n-by-n matrix A is contained in the unit disk D‾ and intersects with the unit circle at more than n points, then W(A)=D‾. An analogue of this result for compact A in an infinite dimensional setting was established by Gau and Wu. We consider here the case of A being the sum of a normal and compact operator.

Original languageEnglish (US)
Pages (from-to)349-353
Number of pages5
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number1
DOIs
StatePublished - May 1 2018

Keywords

  • Compact operator
  • Normal operator
  • Numerical range
  • Weighted shift

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A note on Anderson's theorem in the infinite-dimensional setting'. Together they form a unique fingerprint.

  • Cite this