Perhaps the Simplest Proofs of the Lieb and Lindblad Joint Convexity Inequalities, and More
نویسنده
چکیده
Several important non-commutative inequalities are proved by using Hansen and Pedersen’s Jensen inequality. This approach is also used to demonstrate a matrix analogue of Maréchal’s generalized perspective construction for convex functions.
منابع مشابه
E. Lieb convexity inequalities and noncommutaive Bernstein inequality in Jordan-algebraic setting
We describe a Jordan-algebraic version of E. Lieb convexity inequalities. A joint convexity of Jordan-algebraic version of quantum entropy is proven. A version of noncommutative Bernstein inequality is proven as an application of one of convexity inequalities. A spectral theory on semi-simple complex algebras is used as a tool to prove the convexity results. Possible applications to optimizatio...
متن کاملLieb ’ s simple proof of concavity of ( A , B ) 7 → Tr A p K † B 1 − p K and remarks on related inequalities
A simple, self-contained proof is presented for the concavity of the map (A,B) 7→ TrApK†B1−pK. The author makes no claim to originality; this note gives Lieb’s original argument in its simplest, rather than its most general, form. A sketch of the chain of implications from this result to concavity of A 7→ Tr eK+logA is then presented. An independent elementary proof is given for the joint conve...
متن کامل(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities
In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...
متن کاملInformation-Theoretic Perspectives on Brascamp-Lieb Inequality and Its Reverse
We introduce an inequality which may be viewed as a generalization of both the Brascamp-Lieb inequality and its reverse (Barthe’s inequality), and prove its information-theoretic (i.e. entropic) formulation. This result leads to a unified approach to functional inequalities such as the variational formula of Rényi entropy, hypercontractivity and its reverse, strong data processing inequalities,...
متن کاملHermite-Hadamard Type Inequalities for MφA-Convex Functions
This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008