Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 560580
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 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
  • [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,
  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B25, 47B50

Retrieve articles in all journals with MSC: 47B25, 47B50

Additional Information

Keywords: J-symmetric operators, J-selfadjoint extension, conjugate-linear operator
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society