Gowda, Huche; Lokesha, V. Adjoint-abelian and iso-abelian operators on Banach spaces. (English) Zbl 1026.47001 Adv. Stud. Contemp. Math., Pusan 4, No. 2, 165-172 (2002). Let \(X\) be a Banach space. An operator \(T\) on \(X\) is said to be an adjoint-abelian operator if \(T^*\varphi=\varphi T\), where \(\varphi:X\to X^*\) is a duality mapping, and \(T^*\) is the adjoint of \(T\). An invertible operator \(T\) is said to be iso-abelian if there is a duality mapping \(\varphi\) such that \(\varphi T=T^{*-1} \varphi\).In this paper, certain properties of these operators are studied. For example: If \(X\) is smooth, strictly convex and reflexive, and \(T\) is adjoint-abelian, then \(T\) is adjoint-abelian, too. Or: If \(X\) is strictly convex and reflexive and \(T\) is iso-abelian, then the residual spectrum of \(T\) coincides with its approximate point spectrum. Reviewer: József Sándor (Cluj-Napoca) Cited in 1 Review MSC: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 46C15 Characterizations of Hilbert spaces 47A10 Spectrum, resolvent Keywords:adjoint-abelian operator; iso-abelian PDFBibTeX XMLCite \textit{H. Gowda} and \textit{V. Lokesha}, Adv. Stud. Contemp. Math., Pusan 4, No. 2, 165--172 (2002; Zbl 1026.47001)