A generalization of the Chandler Davis convexity theorem
نویسندگان
چکیده
منابع مشابه
A generalization of the Chandler Davis convexity theorem
In 1957 Chandler Davis proved a theorem that a rotationally invariant function on symmetric matrices is convex if and only if it is convex on the diagonal matrices. We generalize this result to groups acting nonlinearly on convex subsets of arbitrary vector spaces thereby understanding the abstract mechanism behind the classical theorem. We apply the new theorem to a problem from the mathematic...
متن کاملAnother Simple Proof of a Theorem of Chandler Davis
In 1957, Chandler Davis proved that unitarily invariant convex functions on the space of hermitian matrices are precisely those which are convex and symmetrically invariant on the set of diagonal matrices. We give a simple perturbation theoretic proof of this result. (Davis’ argument was also very short, though based on completely different ideas). Consider an orthogonally invariant function f ...
متن کاملDavis’ Convexity Theorem and Extremal Ellipsoids
We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article. MSC 2000: 52A27, 52A20
متن کاملA GENERALIZATION OF A JACOBSON’S COMMUTATIVITY THEOREM
In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.
متن کاملA Generalization of Lyapounov's Convexity Theorem to Measures with Atoms
The distance from the convex hull of the range of an n-dimensional vector-valued measure to the range of that measure is no more than an/2, where a is the largest (one-dimensional) mass of the atoms of the measure. The case a = 0 yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2005
ISSN: 0196-8858
DOI: 10.1016/j.aam.2004.09.001