Some inequalities for positive linear maps

Bhatia, Rajendra ; Sharma, Rajesh (2012) Some inequalities for positive linear maps Linear Algebra and its Applications, 436 (6). pp. 1562-1571. ISSN 0024-3795

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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 2×2 matrices. A noncommutative analogue of the variance is studied, and a basic inequality, with several applications, is established.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Positive Unital Linear Map; Convex Function; Jensen’s Inequality; Variance; Spread; Condition Number
ID Code:97489
Deposited On:20 Feb 2013 10:01
Last Modified:20 Feb 2013 10:01

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