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 $\$\; \backslash mathcal\; M\; \$$ 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 $\$\; \backslash mathcal\; M\; \$$.

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Last modified: December 23, 2001