The upper Browder spectrum property

The upper Browder spectrum property In this note we continue our study on the upper Browder spectrum initiated in Benjamin and Mouton (Quaest. Math. 39(5), 2016). Recall that, for an element a of an ordered Banach algebra A and w.r.t. a Banach algebra homomorphism $$T: A \rightarrow B,$$ T : A → B , we have inclusions $$\begin{aligned} \sigma (Ta) \subseteq \beta _T(a) \subseteq \beta _T^+(a) \subseteq \sigma (a), \end{aligned}$$ σ ( T a ) ⊆ β T ( a ) ⊆ β T + ( a ) ⊆ σ ( a ) , where $$\sigma (Ta),$$ σ ( T a ) , $$\beta _T(a),$$ β T ( a ) , $$ \beta _T^+(a)$$ β T + ( a ) and $$ \sigma (a)$$ σ ( a ) denote the Fredholm, Browder, upper Browder and (usual) spectra of a,  respectively (Benjamin and Mouton in Quaest. Math. 39(5), 2016). This paper concerns the following natural question: given that the spectral radius of a positive element is not in the Fredholm spectrum of the element, when will it be outside the upper Browder spectrum of that element? Positivity Springer Journals

The upper Browder spectrum property

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Springer International Publishing
Copyright © 2016 by Springer International Publishing
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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