Restricted unitary group
= Restricted unitary group
{title2=$U_{\mathrm{res}}(H,P)=\{u:[P,u]\in\mathcal S_2\}$}
For an orthogonal projection $P$ on a complex <Hilbert space>, this is the group of unitary operators whose off-diagonal blocks relative to $PH\oplus(I-P)H$ are <Hilbert-Schmidt operators>. Its usual topology combines strong operator convergence with Hilbert-Schmidt convergence of $[P,u]$. It is the group implementable in the corresponding <polarized fermionic Fock space>.