Invariant Lagrangian subspaces

Andersson, Lars

doi:10.1090/S0002-9939-1988-0954992-7

Invariant Lagrangian subspaces

Author: Lars Andersson
Journal: Proc. Amer. Math. Soc. 103 (1988), 1113-1119
MSC: Primary 47B50; Secondary 47A15, 58F05, 58G15
DOI: https://doi.org/10.1090/S0002-9939-1988-0954992-7
MathSciNet review: 954992
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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
[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
[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
[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
[5] Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
Michael Reed and Barry Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0493420
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
[6] R. C. Swanson, Linear symplectic structures on Banach spaces, Rocky Mountain J. Math. 10 (1980), no. 2, 305–317. MR 575305, https://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, https://doi.org/10.1016/0001-8708(71)90020-X
[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