Li, Shaokuan An inequality for positive operators in Krein spaces. (Chinese) Zbl 0796.47025 Chin. Ann. Math., Ser. A 13, No. 4, 479-481 (1992). Let \(K\) be a Krein space. Let \(P\) be a positive operator acting on \(K\) and \(A\) be an operator commuting with \(P\). The author gives an inequality of the form \(A^ + PA\leq r_{sp}(A^ + A)P\), where \(A^ +\) is the dual operator of \(A\) with respect to the indefinite inner product in \(K\) and \(r_{sp} (A^ +A)\) is the spectral radius of \(A^ + A\). This inequality is also used to give a new proof of a known result concerning the complementation of subspaces in \(K\). Reviewer: Hou Jinchuan (Linfen) MSC: 47B50 Linear operators on spaces with an indefinite metric 46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) 47A63 Linear operator inequalities Keywords:operator inequality; Krein space; positive operator; dual operator; indefinite inner product; complementation of subspaces PDFBibTeX XMLCite \textit{S. Li}, Chin. Ann. Math., Ser. A 13, No. 4, 479--481 (1992; Zbl 0796.47025)