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Proceedings of the American Mathematical Society

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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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Abstract: It is proved that on Hilbert spaces with strong symplectic form, every symplectic operator $ I + C$ with $ C$ compact has an invariant Lagrangian subspace.

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  • [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. 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, 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
  • [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

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Keywords: Invariant subspace, symplectic transformation
Article copyright: © Copyright 1988 American Mathematical Society