Geodesic
Extension theory for operators and spaces with indefinite metric
Izvestiya. Mathematics , Tome 8 (1974) no. 4, pp. 895-907.

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We show that the classical extension theory for isometric operators cannot be automatically extended to $J$-isometric and $J$-Hermitian operators in $J$-spaces with infinite rank. We construct a single extension theory which includes both the isometric and Hermitian operators in a Hilbert space and the $J$-isometric and $J$-Hermitian operators in a $J$-space with arbitrary indefinite rank. The basis of the construction is a scheme for extension of a neutral subspace of a $J$-space to a maximal or hypermaximal subspace. 
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Yu. L. Shmul'yan. Extension theory for operators and spaces with indefinite metric. Izvestiya. Mathematics , Tome 8 (1974) no. 4, pp. 895-907. http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a5/

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