Abstract
Let T be a linear operator whose domain D (T) and range R (T) both lie in the same complex linear topological space X. We consider the linear operator
where λ is a complex number and I the identity operator. The distribution of the values of λ for which T λ has an inverse and the properties of the inverse when it exists, are called the spectral theory for the operator T. We shall thus discuss the general theory of the inverse of T λ .
Keywords
- Linear Operator
- Periodic Function
- Continuous Linear Operator
- Operational Calculus
- Linear Topological Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Comments and References
Phillips, R. S. The adjoint semi-group. Pacific J. Math. 5, 269–283 (1955).
Nagumo, M. Einige analytische Untersuchungen in linearen metrischen Ringen. Jap. J. Math. 13, 61–80 (1936).
Taylor, A. Introduction to Functional Analysis, Wiley 1958.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1968 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yosida, K. (1968). Resolvent and Spectrum. In: Functional Analysis. Die Grundlehren der mathematischen Wissenschaften, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11791-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-11791-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11793-4
Online ISBN: 978-3-662-11791-0
eBook Packages: Springer Book Archive