(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 3, PAGES 925-930

## An approximation modulo $s$2 of isometrical operators and cocycle conjugacy of endomorphisms of the CAR algebra

G. G. Amosov

Abstract

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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 $II$1 and type $III$l 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 $\mathcal M$.

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