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

被引：4

作者：

Birbonshi, Riddhick ^{[1
]}

Spitkovsky, Ilya M. ^{[2
]}

Srivastava, P. D. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Kharagpur 721302, W Bengal, India

[2] NYUAD, Div Sci & Math, POB 129188, Abu Dhabi, U Arab Emirates

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 461卷 / 01期

关键词：

Numerical range; Normal operator; Compact operator; Weighted shift; NUMERICAL RANGE; WEIGHTED SHIFT; SPECTRUM;

D O I：

10.1016/j.jmaa.2018.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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) over bar and intersects with the unit circle at more than n points, then W(A) = (D) over bar. 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. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：349 / 353

页数：5

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