Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces.
We prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.
Piccione
Paolo
P
Departamento de Matemática, Universidade de São Paulo, 05508-900 São Paulo, SP, Brazil. piccione@ime.usp.br
Tausk
Daniel V
DV