Abstract
Let us begin with the following well-known result (see, e.g., [20], Chapter 1, §5).
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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]).
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© 1995 Springer Science+Business Media Dordrecht
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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
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DOI: https://doi.org/10.1007/978-94-015-8561-3_6
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