Abstract
It is often useful to ask of a point in the spectrum of an operator how it got there. To say that A is in the spectrum of A means that A — λ is not invertible. The question reduces therefore to this: why is a non-invertible operator not invertible? There are several possible ways of answering the question; they have led to several (confusingly overlapping) classifications of spectra.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Halmos, P.R. (1982). Properties of Spectra. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9330-6_9
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9330-6_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9332-0
Online ISBN: 978-1-4684-9330-6
eBook Packages: Springer Book Archive