Boulmaarouf, Zineb The Laffey-West decomposition. (English) Zbl 0675.47008 Proc. R. Ir. Acad., Sect. A 88, No. 2, 125-131 (1988). Let \(X\) be a real or complex Banach space and let \(L(X)\) denote the set of all bounded linear operators from \(X\) into itself. The following theorem is proved: If \(A\in L(X)\) is an Atkinson operator with index \(i(A)=0\) \((>0;<0)\) then for each \(n\in\mathbb N\) there exists \(V_ n\in L(X)\), invertible (right invertible; left invertible) and there exists \(F_ n\in L(X)\), of finite rank, such that (a) \(A=V_ n+F_ n\) and (b) for each \(j\in \mathbb N\), \(j\leq n\Rightarrow [F_ n,[A^ j,F_ n]]=0\). This theorem generalises a similar result for Fredholm operators of T. J. Laffey and T. T. West [Proc. R. Ir. Acad. 82A, 129–140 (1982; Zbl 0479.47009)]. Reviewer: R. Gross Cited in 2 Documents MSC: 47A53 (Semi-) Fredholm operators; index theories Keywords:Atkinson operator; right invertible; left invertible Citations:Zbl 0479.47009 PDFBibTeX XMLCite \textit{Z. Boulmaarouf}, Proc. R. Ir. Acad., Sect. A 88, No. 2, 125--131 (1988; Zbl 0675.47008)