### 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 language | English (US) |
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Pages (from-to) | 349-353 |

Number of pages | 5 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 461 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2018 |

### Keywords

- Compact operator
- Normal operator
- Numerical range
- Weighted shift

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Birbonshi, R., Spitkovsky, I. M., & Srivastava, P. D. (2018). A note on Anderson's theorem in the infinite-dimensional setting.

*Journal of Mathematical Analysis and Applications*,*461*(1), 349-353. https://doi.org/10.1016/j.jmaa.2018.01.002