The Pair of Operators $${T^{\stackrel{[\!*\!]}{}}T}$$ and $${TT^{\stackrel{[\!*\!]}{}}}$$ : J-Dilations and Canonical Forms

André C M Ran,Michał Wojtylak

doi:10.1007/s00020-010-1830-7

The Pair of Operators $${T^{\stackrel{[\!\!]}{}}T}$$ and $${TT^{\stackrel{[\!\!]}{}}}$$ : J-Dilations and Canonical Forms

André C M Ran, Michał Wojtylak

Open Access

https://doi.org/10.1007/s00020-010-1830-7

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Journal: Integral Equations and Operator Theory	Publication Date: Oct 7, 2010
Citations: 2	License type: cc-by-nc

Affiliation: Vrije Universiteit Amsterdam, Institute of Mathematics, Jagiellonian University

#Dimensional Space #Infinite Dimensional Space + Show 8 more

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Abstract

We describe a procedure of dilating an operator T in an infinite dimensional Krein space, such that many of the spectral and algebraic properties of the operators ${T^{\stackrel{[\!*\!]}{}}T}$ and ${TT^{\stackrel{[\!*\!]}{}}}$ are preserved. We use the procedure to study canonical forms of those two operators in a finite dimensional Krein space.

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