Title: Doubly Stochastic Operators and Majorization of Integrable Functions

Abstract:

Majorization theory is considered as a powerful tool in application, especially in quantum physics. Since many quantum problems occur in the in_nite dimension, many mathematicians, such as Ryff and Day, generalized the Majorization theory based on doubly stochastic operators to in_nite dimensional space. In this talk, we introduce larger class of operators on L1(X; _) which is more suitable for extending the notion of majorization, called semi doubly stochastic operators. We show that on the _nite measure space (X; _), doubly stochastic operators and semi doubly stochastic operators on L1(X; _) coincide, but in general we provide a counterexample.