The Radon–Nikodym problem for approximately proper equivalence relations

The Radon-Nikodym problem for approximately proper equivalence relations

The Radon-Nikodym problem for approximately proper equivalence relations

We study the Radon-Nikodym problem for approximately proper equivalence relations and more specifically the uniqueness of certain Gibbs states. One of our tools is a variant of the dimension group introduced in the study of AF algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the PerronFrobenius-Ruelle theorem.

un 2 00 2 C * - Algebras , Approximately Proper Equivalence Relations , and Thermodynamic

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a " quotient space ". We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from Thermodynamics we prove that these states are unique as w...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Equivalence Relations and the Halting Problem

We investigate which computable equivalence structures are isomorphic relative to the Halting problem.