Abstract
In the present chapter, spectral mapping theorems will be established for hyponormal operators under a special class of functional transformations
and for semi-hyponormal operators under another class of functional transformations
These classes of functional transformations are closely related with those properties of hyponormal operators (or semi-hyponormal operators which are connected with the Cartesian decomposition or the polar decomposition, respectively. It is expected that some theory will appear for more general functional transformations.
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References
For the references concerned with the function class S(E), see Donoghue [1]; for theorem 1.2, see Xia and Li [1].
For theorem 2.3, see Xia and Li [1]. Theorem 2.5 and corollary 2.6 are published here for the first time. The reference concerned is Xia [10].
For theorems 3.1–2, see Xia and Li [2]; for lemma 3.3 and theorem 3.4, see Xia [10]; for theorems 3–9–10, see Li [7].
Theorem 4.3 is published here for the first time.
For theorem 5.1, see Li [1], Xia and Li [1,2]. Xia [6] introduced the concept of quasinormal operators and listed some of their properties.
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© 1983 Springer Basel AG
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Xia, D. (1983). Spectral Mapping. In: Spectral Theory of Hyponormal Operators. Operator Theory: Advances and Applications, vol 10. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5435-1_6
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DOI: https://doi.org/10.1007/978-3-0348-5435-1_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5437-5
Online ISBN: 978-3-0348-5435-1
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