Von Neumann algebras and projections in space with conjugation operator (Q2263083)

The paper is devoted to algebras of operators on spaces with indefinite metrics. Let \(B(H)\) be the set of all bounded operators on \(H\). Let \(J\) be a conjugation operator in \(H\), i.e., (1) \(J^2=I\), (2) \((Jx,Jy)=(y,x)\) for all \(x,y\in H\). In this paper, the author gives a classification of von Neumann algebras in a Hilbert space with conjugation operator and studies \(J\)-projections in von~Neumann \(J\)-algebras of so-called type \((B)\) [\textit{M. M. Mel'tser}, Funct. Anal. Appl. 13, 305--307 (1980), translation from Funkts. Anal. Prilozh. 13, No. 4, 83--84 (1979; Zbl 0434.46041)].