Entropy for canonical shifts
Author:
Marie Choda
Journal:
Trans. Amer. Math. Soc. 334 (1992), 827-849
MSC:
Primary 46L55; Secondary 46L35
DOI:
https://doi.org/10.1090/S0002-9947-1992-1070349-0
MathSciNet review:
1070349
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Abstract | References | Similar Articles | Additional Information
Abstract: For a -endomorphism
of an injective finite von Neumann algebra
, we investigate the relations among the entropy
for
, the relative entropy
of
for
, the generalized index
, and the index for subfactors. As an application, we have the following relations for the canonical shift
for the inclusion
of type II
factors with the finite index
,
![$\displaystyle H(A\vert\Gamma (A)) \leq 2H(\Gamma ) \leq \log \lambda {(A,\Gamma (A))^{ - 1}} = 2\log [M:N],$](images/img22.gif)



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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1992-1070349-0
Article copyright:
© Copyright 1992
American Mathematical Society