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On $ J$-selfadjoint extensions of $ J$-symmetric operators


Author: Ian Knowles
Journal: Proc. Amer. Math. Soc. 79 (1980), 42-44
MSC: Primary 47B25; Secondary 47B50
DOI: https://doi.org/10.1090/S0002-9939-1980-0560580-X
MathSciNet review: 560580
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Abstract: A short proof is given (via the theory of conjugate-linear operators) of the fact that every J-symmetric operator in a Hilbert space $ \mathcal{K}$ has a J-selfadjoint extension in $ \mathcal{K}$.


References [Enhancements On Off] (What's this?)

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
    Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Spectral theory. Selfadjoint operators in Hilbert space; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1963 original; A Wiley-Interscience Publication. MR 1009163
    Nelson Dunford and Jacob T. Schwartz, Linear operators. Part III, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Spectral operators; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1971 original; A Wiley-Interscience Publication. MR 1009164
  • [2] Alberto Galindo, On the existence of 𝐽-selfadjoint extensions of 𝐽-symmetric operators with adjoint, Comm. Pure Appl. Math. 15 (1962), 423–425. MR 0149305, https://doi.org/10.1002/cpa.3160150405
  • [3] I. M. Glazman, An analogue of the extension theory of Hermitian operators and a non-symmetric one-dimensional boundary problem on a half-axis, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 214–216 (Russian). MR 0091440

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560580-X
Keywords: J-symmetric operators, J-selfadjoint extension, conjugate-linear operator
Article copyright: © Copyright 1980 American Mathematical Society