Unitary operators in the orthogonal complement of a type $\mathrm{I}$ von Neumann algebra in a type ${\mathrm{II}}_1^{}$ factor

Xiaoyan Zhou, Rui Shi

It is well-known that the equality $$L_G^{}\ominus L_H^{}=\overline{\mathrm{span}\{L_g:g\in G-H{\}}^{\mathrm{SOT}}}$$ holds for $G$ an i.c.c. group and $H$ a subgroup in $G$, where…