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This article is cited in 5 scientific papers (total in 5 papers)
Extension theory for operators and spaces with indefinite metric
Yu. L. Shmul'yan
Abstract:
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.
Received: 26.02.1973
Citation:
Yu. L. Shmul'yan, “Extension theory for operators and spaces with indefinite metric”, Izv. Akad. Nauk SSSR Ser. Mat., 38:4 (1974), 896–908; Math. USSR-Izv., 8:4 (1974), 895–907
Linking options:
https://www.mathnet.ru/eng/im1994https://doi.org/10.1070/IM1974v008n04ABEH002131 https://www.mathnet.ru/eng/im/v38/i4/p896
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Abstract page: | 335 | Russian version PDF: | 183 | English version PDF: | 14 | References: | 35 | First page: | 1 |
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