非线性单调正映射
Non-linear monotone positive maps
摘要：
研究了C* 代数之间的几类一般非线性正映射，它们不一定是完全正映射.本文将 *-乘法映射与正线性映射的合成类刻划为有界正型抽象的非线性映射类。本文考虑了三类只定义在正锥上的非线性正映射，它们分别是单调映射、超同余映射和凹映射。任何凹映射都是单调的。单调映射与超同余映射的交刻画了单调Borel谓词演算类.我们给出了许多非线性正映射的例子，表明这三类映射之间一般不存在其它关系。
英文摘要：
We study several classes of general non-linear positive maps between C*-algebras, which are not necessary completely positive maps. We characterize the class of the compositions of *-multiplicative maps and positive linear mapsas the class of non-linear maps of boundedly positive type abstractly. We consider three classes of non-linear positive maps defined only on the positive cones, which are the classes of being monotone, supercongruent or concave. Any concave maps are monotone. The intersection of the monotone maps and the supercongruent maps characterizes the class of monotone Borel functional calculus. We give many examples of non-linear positive maps, which show that there exist no other relations among these three classes in general.
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