An approximation modulo $s_2$ of isometrical operators and cocycle conjugacy of endomorphisms of the CAR algebra

We investigate the possibility of approximation modulo $s_2$ of isometrical operators in Hilbert space. Further we give the criterion of innerness of quasifree automorphisms of hyperfinfite factors $\mathcal M$ of type $\mathrm{II}_1$ and type $\mathrm{III}_{\lambda }$ generated by the representations of the algebra of canonical anticommutation relations (CAR). The results are used to describe cocycle conjugacy classes of quasifree shifts on hyperfinite factors of $\mathcal M$.