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An inequality for positive operators in Krein spaces. (Chinese) Zbl 0796.47025

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 \(K\).

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
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