English

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

Functional Analysis 2017-05-24 v1

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 and intersects with the unit circle at more than n points, then it coincides with the (closed) unit dissk. 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.

Keywords

Cite

@article{arxiv.1705.08223,
  title  = {A note on Anderson's theorem in the infinite-dimensional setting},
  author = {Riddhick Birbonshi and Ilya M. Spitkovsky and P. D. Srivastava},
  journal= {arXiv preprint arXiv:1705.08223},
  year   = {2017}
}

Comments

5 pages

R2 v1 2026-06-22T19:56:12.615Z