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

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

doi:10.1016/j.jmaa.2018.01.002

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	349-353
Number of pages	5
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.01.002
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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10.1016/j.jmaa.2018.01.002

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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.",

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AU - Spitkovsky, Ilya M.

AU - Srivastava, P. D.

N1 - Funding Information: The second author was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi. Publisher Copyright: © 2018 Elsevier Inc.

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AB - 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.

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KW - Normal operator

KW - Numerical range

KW - Weighted shift

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

Abstract

Keywords

ASJC Scopus subject areas

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