151. Some inequalities for positive linear maps
- Author
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Bhatia, Rajendra and Sharma, Rajesh
- Subjects
- *
MATHEMATICAL inequalities , *LINEAR operators , *MATRICES (Mathematics) , *CONVEX functions , *NONCOMMUTATIVE algebras , *MATHEMATICAL analysis , *ANALYSIS of variance - Abstract
Abstract: It has long been known that an analogue of Jensen’s inequality holds for positive unital linear maps on matrix algebras provided that instead of ordinary convex functions one restricts to matrix convex functions. We show that this restriction is not necessary in the case of matrices. A noncommutative analogue of the variance is studied, and a basic inequality, with several applications, is established. [Copyright &y& Elsevier]
- Published
- 2012
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