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Invariant Lagrangian subspaces
Author:
Lars Andersson
Journal:
Proc. Amer. Math. Soc. 103 (1988), 1113-1119
MSC:
Primary 47B50; Secondary 47A15, 58F05, 58G15
MathSciNet review:
954992
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Additional Information
Abstract: It is proved that on Hilbert spaces with strong symplectic form, every symplectic operator  with  compact has an invariant Lagrangian subspace.
- [1]
William
B. Arveson and Jacob
Feldman, A note on invariant subspaces, Michigan Math. J.
15 (1968), 61–64. MR 0223922
(36 #6969)
- [2]
J.
J. Duistermaat, Fourier integral operators, Courant Institute
of Mathematical Sciences, New York University, New York, 1973. Translated
from Dutch notes of a course given at Nijmegen University, February 1970 to
December 1971. MR 0451313
(56 #9600)
- [3]
Pierre
de la Harpe, Classical Banach-Lie algebras and Banach-Lie groups of
operators in Hilbert space, Lecture Notes in Mathematics, Vol. 285,
Springer-Verlag, Berlin-New York, 1972. MR 0476820
(57 #16372)
- [4]
Stephen
M. Paneitz, Hermitian structures on solution varieties of nonlinear
relativistic wave equations, Differential geometric methods in
mathematical physics (Clausthal, 1980), Lecture Notes in Math.,
vol. 905, Springer, Berlin-New York, 1982, pp. 108–118. MR 657446
(83g:81048)
- [5]
Michael
Reed and Barry
Simon, Methods of modern mathematical physics. IV. Analysis of
operators, Academic Press [Harcourt Brace Jovanovich, Publishers], New
York-London, 1978. MR 0493421
(58 #12429c)
- [6]
R.
C. Swanson, Linear symplectic structures on Banach spaces,
Rocky Mountain J. Math. 10 (1980), no. 2,
305–317. MR
575305 (81j:58014), http://dx.doi.org/10.1216/RMJ-1980-10-2-305
- [7]
Alan
Weinstein, Symplectic manifolds and their Lagrangian
submanifolds, Advances in Math. 6 (1971),
329–346 (1971). MR 0286137
(44 #3351)
- [8]
N.
M. J. Woodhouse, Geometric quantization, 2nd ed., Oxford
Mathematical Monographs, The Clarendon Press, Oxford University Press, New
York, 1992. Oxford Science Publications. MR 1183739
(94a:58082)
- [1]
- W. B. Arveson and J. Feldman, A note on invariant subspaces, Michigan Math. J. 15 (1967), 61-64. MR 0223922 (36:6969)
- [2]
- J. J. Duistermaat, Fourier integral operators, Courant Institute Lecture Note, New York Univ., 1973. MR 0451313 (56:9600)
- [3]
- P. Harpe, Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lecture Notes in Math., vol. 285, Springer-Verlag, Berlin, 1972. MR 0476820 (57:16372)
- [4]
- S. M. Paneitz, Hermitian structures on solution varieties of nonlinear relativistic wave equations, Lecture Notes in Math., vol. 905, Springer-Verlag, Berlin, 1980, 108-118. MR 657446 (83g:81048)
- [5]
- M. Reed and B. Simon, Analysis of operators, Methods of Modern Mathematical Physics, 4, Academic Press, New York, 1978. MR 0493421 (58:12429c)
- [6]
- R. C Swanson, Linear symplectic structures on Banach spaces, Rocky Mountain J. Math. 10 (1980), 305-317. MR 575305 (81j:58014)
- [7]
- A. Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Adv. in Math. 6 (1971), 329-346. MR 0286137 (44:3351)
- [8]
- N. M. J. Woodhouse, Geometric quantization, Clarendon Press, Oxford, 1980. MR 1183739 (94a:58082)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0954992-7
PII:
S 0002-9939(1988)0954992-7
Keywords:
Invariant subspace,
symplectic transformation
Article copyright:
© Copyright 1988
American Mathematical Society
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