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Published in:
Preliminaries Read chapter Read first chapter

2018 | OriginalPaper | Chapter

5. Seminormality

Authors : Piotr Budzyński, Zenon Jabłoński, Il Bong Jung, Jan Stochel

Published in: Unbounded Weighted Composition Operators in L²-Spaces

Publisher: Springer International Publishing

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Abstract

In this chapter, we give characterizations of seminormal, formally normal, symmetric, selfadjoint and positive selfadjoint weighted composition operators. Hyponormality and cohyponormality are characterized in Sects. 5.1 and 5.2, respectively (see Theorems 53 and 60). The introductory part of Sect. 5.2 is devoted to the study of the range of the conditional expectation E ϕ,w. In Sect. 5.3, we characterize normal weighted composition operators (see Theorem 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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Footnotes
1
In the condition (i) (see also Corollary 70(i)), the expression “for all f ∈ L 2(τ)” should be understood as “for all \(\mathcal A\)-measurable functions \(f\colon X \to \mathbb C\) such that ∫ X | f|2dτ < ∞”.
 
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Metadata
Title
Seminormality
Authors
Piotr Budzyński
Zenon Jabłoński
Il Bong Jung
Jan Stochel
Copyright Year
2018
Book
Unbounded Weighted Composition Operators in L²-Spaces

Print ISBN: 978-3-319-74038-6

Electronic ISBN: 978-3-319-74039-3

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-74039-3_5

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