Fredholm Composition Operators on Non-atomic Measure Space
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,φ,u) is non-atomic. The existence condition of Fredholm operator is discussed.
In this paper, we obtain a $\alpha$-Suzuki fixed point theorem by using $C$ - class function on quasi metric spaces. Also we give an example which supports our main theorem.