非原子测度空间上的Fredholm复合算子

Fredholm Composition Operators on Non-atomic Measure Space

算子的Fredholm性质、本性酉、本性正规性的研究长期受关注,特别是Fredholm算子在什么条件下是可逆算子一直是Fredholm算子研究的中心问题.讨论了非原子测度空间(X,φ,u)上L2(u)上的复合算子的Fredholm的本性酉、本性正规等性质以及Fredholm算子存在的条件.

The Fredholm property of operator, essentially unitary and essentially normal composition are important. Which Fredholm operator are reversible operator is the key problem. The main purpose of this paper is to study Fredholm, essentially unitary and essentially normal composition operators on L^2 （ u ） when the underlying measure space （ X,ψ,u） is non-atomic. The existence condition of Fredholm operator is discussed.