Abstract
Let us begin with the following well-known result (see, e.g., [20], Chapter 1, §5).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
The results of Chapters 6 and 7 were obtained by M.S.Livšic and A.S.Markus [43].
The definitions of joint spectra (σl, σr, σ) were introduced in [25]. The spectral mapping theorem (Theorem 5.2.1) was also established there (see [26] as well). The left joint spectrum was considered earlier [9] (under different name), and its non-emptiness was proved.
The spectral mapping theorem for rational functions (Theorem 5.2.4) was proved in [11] (see also [13]). Various generalizations for Banach spaces are also contained there (see also [53]).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Livšic, M.S., Kravitsky, N., Markus, A.S., Vinnikov, V. (1995). Joint Spectrum of Commuting Operators with Compact Imaginary Parts. In: Theory of Commuting Nonselfadjoint Operators. Mathematics and Its Applications, vol 332. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8561-3_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-8561-3_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4585-0
Online ISBN: 978-94-015-8561-3
eBook Packages: Springer Book Archive