Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces

Anais da Academia Brasileira de Ciências

Paolo Piccione¹  Daniel V. Tausk¹ 

[1] ,Universidade de São Paulo Departamento de Matemática São Paulo SP ,Brasil

关键词: symplectic Hilbert spaces;    Lagrangian subspaces;    Lagrangian Grassmannian;    unbounded self-adjoint operators;    spectral theorem;    Espaços de Hilbert simpléticos;    subespaços Lagrangeanos;    Grassmanniano de Lagrangeanos;    operadores auto-adjuntos ilimitados;    teorema espectral;   

DOI  :  10.1590/S0001-37652005000400002

来源: SciELO

【 摘 要 】

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.

【 授权许可】

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