Rajarajeswari, E. The semigroup of normal singular operators. (English) Zbl 0863.47020 J. Ramanujan Math. Soc. 10, No. 2, 123-140 (1995). Summary: Given a group \(G\) of invertible operators on a locally convex Hausdorff space \(X\) and a continuous projection \(p\) on \(X\) satisfying \([a,p]= ap-pa\) compact, we set \(S(G,p)=\{ap+bq+t:a,b\in G, t\in\widehat K(X)\}\), where \(q=1-p\) and \(\widehat K(X)\) is the set of all compact operators on \(X\). Then \(S(G,p)\) is seen to be a regular monoid.In this paper, we consider some algebraic properties of this semigroup. The study of the index of operators in \(S(G,p)\) gives some useful results, such as: \(S(G,p)\) is simple implies \(k(X)\geq 1\) and \(S(G,p)\) is bisimple implies \(k(X)=1\), where \(k(X)\) is the characteristic number of \(X\), as given in Definition 5.1 of [E. Krishnan and K. S. S. Nambooripad, Forum. Math. 5, No. 4, 313-368 (1993; Zbl 0803.47017)]. MSC: 47D03 Groups and semigroups of linear operators 47A53 (Semi-) Fredholm operators; index theories 45P05 Integral operators Keywords:Fredholm operators; invertible operators; compact operators; regular monoid; index Citations:Zbl 0803.47017 PDFBibTeX XMLCite \textit{E. Rajarajeswari}, J. Ramanujan Math. Soc. 10, No. 2, 123--140 (1995; Zbl 0863.47020)