FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(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 $\mathrm{II}_1$ 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 $\mathcal M$.
```

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Last modified: December 23, 2001