A MICROSTATES APPROACH TO RELATIVE FREE ENTROPY
نویسندگان
چکیده
منابع مشابه
A Microstates Approach to Relative Free Entropy
His approach involved non-commutative Hilbert transform and is algebraic in nature. In the case that B = C, this quantity is denoted χ(X1, . . . , Xn), and its properties are very similar to those of the free entropy χ(X1, . . . , Xn) introduced by Voiculescu in [4] using microstates; in fact, it may very well be that the two quantities coinside. Using the microstates approach to free entropy, ...
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We define an analog of Voiculescu’s free entropy for n-tuples of unitaries u1, . . . , un in a tracial von Neumann algebra M which normalize a unital subalgebra L[0, 1] = B ⊂ M. Using this quantity, we define the free dimension δ0(u1, . . . , un G B). This number depends on u1, . . . , un only up to orbit equivalence over B. In particular, if R is a measurable equivalence relation on [0, 1] gen...
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2002
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x02001411