Abstract
In this Lecture we describe those cases when a “spectral decomposition” of the model operator TΘ is possible, taking these words in a broader sense than in Lectures VI–VIII. In place of eigenspaces we will consider arbitrary spectral (and even more general) subspaces and the corresponding parts of the spectrum σ(TΘ) will be drawn from a specially chosen σ-algebra of Borel sets. We must of course maintain sufficiently tight connections with the classical expansion as provided by the Spectral Theorem for normal operators. The necessary language will be borrowed from the theory of spectral operators in the sense of Dunford, concerning which some notions will be developed in the “Concluding Notes” of this Lecture.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nikol’skiĭ, N.K. (1986). Generalized Spectrality and Interpolation of Germs of Analytic Functions. In: Treatise on the Shift Operator. Grundlehren der mathematischen Wissenschaften, vol 273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70151-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-70151-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-70153-5
Online ISBN: 978-3-642-70151-1
eBook Packages: Springer Book Archive