Invariant Lagrangian subspaces
Invariant Lagrangian subspaces
It is proved that on Hilbert spaces with strong symplectic form, every symplectic operator<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I plus upper C"><mml:semantics><mml:mrow><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:annotation encoding="application/x-tex">I + C</mml:annotation></mml:semantics></mml:math></inline-formula>with<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C"><mml:semantics><mml:mi>C</mml:mi><mml:annotation encoding="application/x-tex">C</mml:annotation></mml:semantics></mml:math></inline-formula>compact has an invariant Lagrangian subspace.