| Popis: |
The main goal of this chapter is to provide criteria for the subnormality of (not necessarily bounded) weighted composition operators. The first criterion, which is given in Sect. 3.1, requires that hϕ,w > 0 a.e. [μ w ] and that there exists a measurable family of Borel probability measures on \(\mathbb R_+\) satisfying the consistency condition (CC) (see Theorem 29). Section 3.3 provides the second criterion which involves another, stronger than (CC), condition (CC−1) (see Theorem 34). In Sect. 3.4, we discuss the interplay between the conditions (CC) and (CC−1) (see Theorem 40). Section 3.2 shows that the consistency condition (CC) itself is not sufficient for subnormality even in the case of composition operators. By Theorem 34, this means that (CC) does not imply (CC−1). |
