自反Banach格上正算子基态的存在性

The existence of ground state for positive operators in reflective Banach lattices

非负算子基态的存在性,是Perron-Frobenius型定理的核心内容,也是证明算子谱缝隙的主要步骤.本文主要利用了正算子非半紧测度的概念,讨论了一般自反Banach格上正算子基态的存在性,并得到了一个充分条件.更为特殊的,若算子同时满足不可约性,证明了基态特征向量是严格正的.

By making use of measure of non-semicompactness,the author gives a sufficient condition for The existence of ground state for positive operators,which is considered crucial for the proof of spectral gap and theorem of Perron-Frobenius type.In addition,if the operator is irreducible,we could prove that the eigenvector is strict positive.