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.
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}
}
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5 pages