Limit Point Analysis of the Browder Spectrum for Operator Matrices
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Authors: A. BAHLOUL
DOI: 10.46793/KgJMat2610.1627B
Abstract:
In this paper, we investigate the limit point set of the Browder spectrum for upper triangular operator matrices ℳ on Banach spaces. Utilizing the robust tools and comprehensive framework of local spectral theory, we offer a detailed analysis of this spectral feature. We establish that the relationship between the accumulation points of the Browder spectrum σBr(ℳ) of ℳ and those of its diagonal entries is encapsulated by the equation:
where 
denotes a specific union of ”holes“ in 
,
comprising subsets within the intersection 
. Furthermore, we
delineate sufficient conditions under which the limit points of the Browder spectrum
for a 3 × 3 upper triangular block operator matrix are precisely characterized as the
union of the limit points of the spectra of its diagonal entries. Our findings
significantly advance the understanding of the spectral properties of operator
matrices, offering crucial insights into their structure within the context of local
spectral theory. Moreover, this work extends and refines the results of A. Tajmouati
et al., as presented in [?], contributing to the ongoing development and enhancement
of operator matrix theory.
Keywords:
Browder spectrum, upper triangular operator matrices, local spectral theory, accumulation points.
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