The restricted Lagrangian Grassmannian in infinite dimension
Manuel L\'opez Galv\'an
TL;DR
This paper investigates the properties of the restricted Lagrangian Grassmannian in infinite-dimensional spaces, focusing on the action of symplectic operators close to the identity.
Contribution
It introduces a detailed analysis of symplectic operator actions on the infinite-dimensional restricted Lagrangian Grassmannian, expanding understanding of its geometric structure.
Findings
Characterization of symplectic operators as perturbations of the identity
Analysis of the geometric structure of the infinite-dimensional Grassmannian
Insights into the action of Hilbert-Schmidt perturbations
Abstract
In this paper we study the action of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator in the Lagrangian Grassmannian manifold.
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