FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

An approximation modulo s2 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 s2 of isometrical operators in Hilbert space. Further we give the criterion of innerness of quasifree automorphisms of hyperfinfite factors $ \mathcal M $ of type II1 and type IIIl 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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