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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Vydané v:	Linear algebra and its applications Ročník 435; číslo 5; s. 1131 - 1136
Hlavní autori:	Wu, Deyu, Chen, Alatancang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Inc 01.09.2011 Elsevier
Predmet:	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
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Shrnutí:	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