Spectral inclusion properties of the numerical range in a space with an indefinite metric

In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums of bounded positive operators (or the spectrum of unbounded uniformly I -positive operators) are contained in the closure of the I -numerical...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 435; no. 5; pp. 1131 - 1136
Main Authors: Wu, Deyu, Chen, Alatancang
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.09.2011
Elsevier
Subjects:
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
The [formula omitted]-numerical range
The indefinite inner product space
The numerical range
The uniformly [formula omitted]-positive operator
47A12
The indefinite inner product space
The uniformly I -positive operator
47B50
The numerical range
The I -numerical range
Closure
Spectral properties
Bounded operator
Indefinite inner product
Spectrum
Prehilbertian space
Numerical range
Indefinite metric
Eigenvalue problem
The G-numerical range
Hausdorff space
The uniformly ?-positive operator
Positive operator
ISSN:0024-3795
Online Access:Get full text
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Summary:In this paper the numerical range of operators (possibly unbounded) in an indefinite inner product space is studied. In particular, we show that the spectrums of bounded positive operators (or the spectrum of unbounded uniformly I -positive operators) are contained in the closure of the I -numerical range.
ISSN:0024-3795
DOI:10.1016/j.laa.2011.02.053