4 problems

Let $G$ be a Banach–Lie group and let $H$ be a closed subgroup. The quotient set $G/H$ is formed from the left cosets $gH$, and the quotient map is … A closed subgroup $H$ of a Ban…

Let ${\mathfrak S}_p({\mathcal H})$ be the Schatten operator ideal on a Hilbert space ${\mathcal H}$, with $1\leq p\leq\infty$. Consider the classical real Banach–Lie groups and al…

Integrability conjecture. The real Banach space $({\mathfrak u}_{{\rm res}})_*$ has a natural structure of Banach Lie–Poisson space and its characteristic distribution is integrabl…

Quotient-manifold criterion. $H$ is a Banach–Lie subgroup if and only if $G/H$ carries the structure of a Banach manifold for which $q$ has a surjective differential at each point…