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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M. Wojtylak would like to express his gratitude for a research position at the Faculty of Sciences of the VU University Amsterdam from 2007 to 2009. The major part of the work has been carried out during that period of time.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ran, A.C.M., Wojtylak, M. The Pair of Operators \({T^{\stackrel{[\!*\!]}{}}T}\) and \({TT^{\stackrel{[\!*\!]}{}}}\): J-Dilations and Canonical Forms. Integr. Equ. Oper. Theory 68, 313–335 (2010). https://doi.org/10.1007/s00020-010-1830-7
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DOI: https://doi.org/10.1007/s00020-010-1830-7