Djordjević, Slaviša; Han, Young Min Browder’s theorems and spectral continuity. (English) Zbl 0979.47004 Glasg. Math. J. 42, No. 3, 479-486 (2000). A bounded operator \(T\) on some complex Banach space is said to obey Browder’s theorem if its Weyl spectrum equals \(\sigma(T)\setminus \pi_0(T)\) with \(\pi_0(T)\) being the set of all normal eigenvalues of \(T\). In this article, the author introduces operators that obey the \(a\)-Browder theorem, a property which turns out to be more restrictive than obeying the usual Browder theorem. On the other hand, by characterizing the operators obeying \(a\)-Browder’s theorem in terms of other spectral data it is shown that quasinilpotent operators, algebraic operators and polynomially Riesz operators all obey the \(a\)-Browder theorem. Moreover, it is proved that if \(a\)-Browder’s theorem holds for \(T\), and \(p\) is any polynomial, then \(p(T)\) obeys \(a\)-Browder’s theorem if and only if \(p(\sigma_{ea}(T))= \sigma_{ea}(p(T))\), where \(\sigma_{ea}\) denotes the essential approximative point spectrum. Reviewer: André Noll (Darmstadt) Cited in 29 Documents MSC: 47A10 Spectrum, resolvent Keywords:bounded operator; Weyl spectrum; normal eigenvalues; \(a\)-Browder theorem; quasinilpotent operators; algebraic operators; polynomially Riesz operators; essential approximative point spectrum PDFBibTeX XMLCite \textit{S. Djordjević} and \textit{Y. M. Han}, Glasg. Math. J. 42, No. 3, 479--486 (2000; Zbl 0979.47004) Full Text: DOI