Open Access
2014 Krein space numerical ranges: compressions and dilations
N. Bebiano, J. da Providencia
Ann. Funct. Anal. 5(1): 36-50 (2014). DOI: 10.15352/afa/1391614567


A criterion for the numerical range of a linear operator acting in a Krein space to be a two-component hyperbolical disc is given, using the concept of support function. A characterization of the Krein space numerical range as a union of hyperbolical discs is obtained by a reduction to the two-dimensional case. We revisit a famous result of Ando concerning the inclusion relation $W(A)\subseteq W(B)$ of the numerical ranges of two operators $A$ and $B$ acting in (possibly different) Hilbert spaces, and the condition that $A$ can be dilated to an operator of the form $B\otimes I$. The extension of this result to operators acting in Krein spaces is investigated.


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N. Bebiano. J. da Providencia. "Krein space numerical ranges: compressions and dilations." Ann. Funct. Anal. 5 (1) 36 - 50, 2014.


Published: 2014
First available in Project Euclid: 5 February 2014

zbMATH: 1302.47057
MathSciNet: MR3119110
Digital Object Identifier: 10.15352/afa/1391614567

Primary: 15A60
Secondary: 15A63 , 46C20

Keywords: compression , dilation , indefinite inner product space , Krein space , numerical range

Rights: Copyright © 2014 Tusi Mathematical Research Group

Vol.5 • No. 1 • 2014
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