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Generalized spectral perturbation and the boundary spectrum
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 603-621
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By considering arbitrary mappings $\omega $ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$, the set $\omega (a)$ lies between the boundary and connected hull of the exponential spectrum of $a$, we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
By considering arbitrary mappings $\omega $ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$, the set $\omega (a)$ lies between the boundary and connected hull of the exponential spectrum of $a$, we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
DOI : 10.21136/CMJ.2021.0046-20
Classification : 46H10, 47A10
Keywords: exponential spectrum; singular spectrum; boundary spectrum; boundary and hull; (strong) Riesz property; Mobius spectrum 
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Mouton, Sonja. Generalized spectral perturbation and the boundary spectrum. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 603-621. doi: 10.21136/CMJ.2021.0046-20

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