Titlebook: Unbounded Weighted Composition Operators in L2-Spaces; Piotr Budzyński,Zenon Jab?oński,Jan Stochel Book 2018 Springer International Publis

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Subnormality: General Criteria,CC.) (see Theorem 34). In Sect. 3.4, we discuss the interplay between the conditions (CC) and (CC.) (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.).

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Seminormality,heorem 63). We also show that formally normal (in particular, symmetric) weighted composition operators are automatically normal (see Theorem 66). In Sect. 5.4, we characterize selfadjoint and positive selfadjoint weighted composition operators (see Theorems 72 and 76).

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0075-8434 eria for subnormality of unbounded weighted composition oper.This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be

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Discrete Measure Spaces, Theorems 89 and 90). The interplay between the theory of moments, the geometry of graphs induced by symbols and the injectivity problem is discussed in Section 6.4 (see Theorem 93 and Problems 96 and 100). Section 6.5 contains a variety of examples illustrating our considerations.

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Subnormality: General Criteria,rion, which is given in Sect. 3.1, requires that ..?>?0 a.e. [..] and that there exists a measurable family of Borel probability measures on . satisfying the consistency condition (CC) (see Theorem 29). Section 3.3 provides the second criterion which involves another, stronger than (CC), condition (

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Discrete Measure Spaces,crete measure spaces. Section 6.1 has an introductory character. Section 6.2 characterizes the hyponormality, cohyponormality and normality of discrete weighted composition operators (see Theorems 83, 84 and 87). Section 6.3 provides two criteria for the subnormality of discrete weighted composition