Operator-valued free Fisher information and modular frames
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- by Bin Meng, Maozheng Guo and Xiaohong Cao PDF
- Proc. Amer. Math. Soc. 133 (2005), 3087-3096 Request permission
Abstract:
We introduce the operator-valued free Fisher information for a random variable in an operator-valued noncommutative probability space and point out its relations to the amalgamated freeness. Using M. Frank and D. Larson’s modular frame notion we can construct the conjugate variable for an operator-valued semicircle variable with conditional expectation covariance. Then we obtain its free Fisher information and show it is equal to the index of the conditional expectation. At last the conjugate variable with respect to a modular frame operator for a semicircle variable is also constructed.References
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Additional Information
- Bin Meng
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Address at time of publication: College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China
- Email: b.meng@nuaa.edu.cn
- Maozheng Guo
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Xiaohong Cao
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Received by editor(s): February 12, 2004
- Received by editor(s) in revised form: June 7, 2004, and June 8, 2004
- Published electronically: April 25, 2005
- Communicated by: David R. Larson
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3087-3096
- MSC (2000): Primary 46L54, 42C15
- DOI: https://doi.org/10.1090/S0002-9939-05-08111-6
- MathSciNet review: 2159789