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I have been reading the article The variation of spectra by J.D Newburgh. in this article and all related reference/ articles, the term 'variation of spectra' keeps coming in, but I nowhere find a formal definition of the term. Can anyone tell me its definition?

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According to the article

"Newburgh, J. D. (1951). The variation of spectra. Duke Mathematical Journal, 18(1), 165–176. doi:10.1215/s0012-7094-51-01813-3"

The variation of spectra is the function $\sigma:A\rightarrow S$, where $A$ is a Banach algebra and $S$ is the metric space of compact subsets of complex plan, $\mathbb C$. The value of this function at point $x\in A$, is $\sigma(x)$, the spectrum of $x$.

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  • $\begingroup$ So it is basically the set valued spectrum function that is upper semicontinuous. Am I right? $\endgroup$
    – user332905
    Commented Mar 27, 2022 at 8:14
  • $\begingroup$ @user332905 if we consider the norm topology on $A$, the answer is "Yes". $\endgroup$
    – MSMalekan
    Commented Mar 27, 2022 at 9:49

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