Year: 2004
Type: article
Abstract: We introduce the operator-valued relative free entropy χ * B (X 1 , X 2 , • • • , Xn : B) of a family of self-adjoint random variables X 1 , X 2 , • • • , Xn in a B-valued noncommutative probability space (A, E B , B).This notion extends D. Voiculescu's relative free entropy Φ * which defined in a tracial W*-noncommutative probability space to a more general context.The free entropy of a semicircular variable with conditional expectation covariance can be computed by using the modular frames and then we point out the relation between the free entropy of a semicircular variable and the index of a conditional expectation.At last, we obtain an estimate of the free entropy dimension δ * B,τ .
Authors: Xiaohong Cao, Maozheng Guo, Bin Meng
Institution: Peking University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1995307231