Abstract
In this chapter we are going to study the trace of a mosaic—the principal function, and to introduce related trace formula and determinant formula.
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References
For the trace and trace operator, also see Gelfand and Velenkin [1].
The Pincus principal functions are derived by Pincus [7] for nearly normal operators (see also Carey and Pincus [9], Helton and Howe [1]). For the main results of the present section, see Pincus and Xia [1].
The main results of the present section can be found in Carey and Pincus [9], Helton and Howe [1,2] and Pincus [7]. The notion of collapsing is due to Pincus.
For theorem 4.2, see Xia [6]. Pincus first considered the determinant of multiplication commutators. For theorem 4.3, see Carey and Pincus [3]. Theorem 4.4 is first published here.
There are some other articles concerned with the present chapter, such as Pincus [1–10], Carey and Pincus [1–12], Apóstol and Clancey [1], Voculescu [1], Curto, Muhly and Xia [1], and so on.
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© 1983 Springer Basel AG
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Xia, D. (1983). Pincus Principal Functions, Traces and Determinants. 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_7
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DOI: https://doi.org/10.1007/978-3-0348-5435-1_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5437-5
Online ISBN: 978-3-0348-5435-1
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