路 *-代数上的正星形与平坦泛函
Positivstellensatz and flat functionals on path *-algebras
摘要：
本文研究一类非交换 *-代数，它们是具有自然对合的箭图的对偶的路代数。研究了这类 *-代数上正截断泛函的扩张问题。本文给出了Curto和Fialkow关于路 *-代数的截断Hamburger矩问题的解的一个类比，并证明了非交换的正定性。我们还对这类代数给出了Curto和Fialkow的平坦扩张定理的一个类比。
英文摘要：
We consider the class of non-commutative *-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such *-algebras. An analog of the solution of the truncated Hamburger moment problem by Curto and Fialkow for path *-algebras is presented and non-commutative positivstellensatz is proved. We aslo present an analog of the flat extension theorem of Curto and Fialkow for this class of algebras.
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