局部凸空间上的Riesz算子

Banach空间中的Riesz算子因其具有与紧算子类似的谱性质而十分重要.由于紧算子的概念已经推广到局部凸空间中去了,经研究,发现同样可以在局部凸空间中讨论Riesz算子的谱理论.本文利用Riesz算子与渐近拟紧算子的等价性来讨论Riesz算子的性质,得到了比较全面的结果.

RIESZ OPERATOR ON LOCALLY CONVEX SPACES

Riesz operators on Banach spaces are very important since its spectral properties are similar to that of compact operators. Now the concept of compact operators are extended onto locally convex spaces. We discovered that we can also study Riesz operators on locally convex spaces. In this paper the author tries to discuss the properties of Riesz operators by means of the equivalence of Riesz operators and asympototically quasi-compact operators, and has attainedto some results almost perfect.