Function Space Operator Sub-operator Algebras

The theory of operator on the function spaces has become an important branch which has played the role of leading the way in modern mathematics and has close and surprised connection with other branches of science such as : quantum mechanics , differential geometry , linear system and control theory , and number theory and so on . It has already been valued by the people more and more , and has already formed a whole and fruitful system of theory now( [1,2,3]) .The studies of composition operators links function theory and operator theory . The main goal is to make use of some results and methods from classical function theory to study some of the most basic questions you can ask about linear operator theory and use operator theory as a tool to study the classical questions on function spaces at the same time . If F is a space of analytic function defined on the unit disk D in complex plane Cand φ is an analytic self-map of D , the linear operator defined byC_φf = f (?)_φ ((?)f∈D),is said to be a composition operator on F . The composition of functions is a fundamental operation on function spaces and has the important application in all mathematics , for example , the composition operator on...