Abstract
We take over the notions defined in Chapter [J I.]. The present is its continuation, or rather a supplement to the theory of the operator φ (N),where φ(z) is a N-measurable complex-valued function of the complex variable z, defined on an N-measurable subset of the complex plane P, and where N is a maximal normal operator in a Hilbert-Hermite-space H. Our purpose is to study the most general operators ψ(φ(N)),φ(ψ(N)) and (φ ψ) (N) — which are not identical and need a quite subtle reasonings — an dapply the results to the general theory of the eigenvalue problem, of the resolvent and of the spectrum of N. We shall show the great adaptability of our theory to that topic, and we shall get a classification of points of the spectrum of normal maximal operators, which seems to be more subtle, than the usual one, (87).
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
© 1966 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Nikodým, O.M. (1966). On items of operational calculus with application to the resolvent and spectrum of normal operators. In: The Mathematical Apparatus for Quantum-Theories. Die Grundlehren der mathematischen Wissenschaften, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46030-2_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-46030-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46032-6
Online ISBN: 978-3-642-46030-2
eBook Packages: Springer Book Archive