FPM 2001, vol. 7, no. 3, pp. 925-930

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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An approximation modulo s2 of isometrical operators and cocycle conjugacy of endomorphisms of the CAR algebra

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