Anderson's theorem for compact operators

Hwa Long Gau; Pei Yuan Wu

doi:10.1090/S0002-9939-06-08699-0

Anderson's theorem for compact operators

Hwa Long Gau, Pei Yuan Wu

Department of Mathematics

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

7 Scopus citations

Abstract

It is shown that if A is a compact operator on a Hilbert space with its numerical range W(A) contained in the closed unit disc double-struck D sign̄ and with W(A) intersecting the unit circle at infinitely many points, then W(A) is equal to double-struck D sign̄. This is an infinite-dimensional analogue of a result of Anderson for finite matrices.

Original language	English
Pages (from-to)	3159-3162
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	134
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-06-08699-0
State	Published - Nov 2006

Keywords

Compact operator
Numerical range

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10.1090/S0002-9939-06-08699-0

Cite this

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AB - It is shown that if A is a compact operator on a Hilbert space with its numerical range W(A) contained in the closed unit disc double-struck D sign̄ and with W(A) intersecting the unit circle at infinitely many points, then W(A) is equal to double-struck D sign̄. This is an infinite-dimensional analogue of a result of Anderson for finite matrices.

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KW - Numerical range

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Anderson's theorem for compact operators

Abstract

Keywords

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