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E. Lieb convexity inequalities and noncommutative Bernstein inequality in Jordan-algebraic setting

Leonid Faybusovich(lfaybuso***at***gmail.com)

Abstract: We describe a Jordan-algebraic version of E. Lieb convexity inequalities. A joint convexity of Jordan-algebraic version of quantum entropy is proven. SA spectral theory on semi-simple complex Jordan algebras is used as atool to prove the convexity results. Possible applications to optimization and statistics are indicated

Keywords: Generalized Convexity, Euclidean Jordan algebras, Quantum Entropy

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 2: Other Topics (Other )

Citation: Preprint, University of Notre Dame, August 2014

Download: [PDF]

Entry Submitted: 08/14/2014
Entry Accepted: 08/14/2014
Entry Last Modified: 08/14/2014

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