Operators In Function Spaces

Research on operator theory in function space is always an important problem in the functional analysis. As a branch of mathematics, it has undergone a long history of study. Moreover, a complete and fruitful system of theory has been formed.Operator in different function space has different characteristics. Studies on operator briefly include boundedness, compactness, spectrum and algebraic( normal and subnormal ) property. Such discussions, with several profound discoveries made already, are mostly carried out on function spaces defined on the unit disc; however, due to the infeasibility of applying classic methodologies directly for investigations, they seldom touch the operators defined on general regions, specifically, operators on multiply connected domains. Fortunately, there may be a way out of this difficulty, since K-theory could manifest potential relation between topological properties of epigraphs and operator properties defined on their topological domains. Therefore, research on operators defined on multiply connected regions whose properties may vary dramatically and relevant K-theory is of significant importance.This paper provides discussion on Toeplitz Operator, Hankel Operator, Composition Operator defined on bounded, multiply connected (multi-connected) regions and properties of their corresponding K-theory, which could be divided into:...