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Some applications of free Fisher information on frame theory |
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| Authors: | Bin Meng Maozheng Guo |
| Institution: | a College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China b School of Mathematical Science, Peking University, Beijing 100871, PR China c College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China |
| Abstract: | We introduce the notion of operator-valued free Fisher information with respect to a positive map of a random variable in an operator-valued noncommutative probability space and point out its close relations to the modular frames arising from conditional expectations. Then we can apply this notion on the study of frame theory, especially on the disjointness problem of modular frames arising from conditional expectations. |
| Keywords: | Conjugate variable Free Fisher information Hilbert _method=retrieve& _eid=1-s2 0-S0022247X05001770& _mathId=si1 gif& _pii=S0022247X05001770& _issn=0022247X& _acct=C000051805& _version=1& _userid=1154080& md5=b5c707c6f4e3f49d1af1d9b7af734c85')" style="cursor:pointer C*-module" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">C*-module Modular frame |
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