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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

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

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