A theorem on the plus-index of a plus-operator (Q2729597)

In a Banach spaces with indefinite metric \({\mathcal B}= {\mathcal B}_+\dot+{\mathcal B}_-\) a bounded operator \(A\) definite on the whole space is named plus-operator if \(A{\mathcal R}_+\subseteq{\mathcal R}_+\), where \({\mathcal R}_+= \{x\in{\mathcal B}\mid\|x_+\|\geq \|x_-\|\}\) is the set of nonnegative vectors. In the article under review the definition of plus-operator \(A\) [\textit{V. A. Khatskevich} and \textit{V. A. Senderov}, Integral Equations Operator Theory 15, No. 5, 784-795 (1992; Zbl 0778.47027)] is given and a theorem about the plus-index of the product \(AB\) of two plus-operators \(A\) and \(B\) is proved.