Order derivations on \(L^ p\)-spaces of \(W^ *\)-algebras
An order derivation is by definition a bounded generator of a one- parameter group of positive operators on an ordered Banach space. In this paper we characterize order derivations on \(L^ p\)-spaces of \(W^ *\)- algebras. In fact we show how order derivations are obtained from the standard representation of the \(W^ *\)-algebra on its \(L^ p\)-space. This makes \textit{A. Connes}'s theory of order derivations on Hilbert spaces in standard forms of \(W^ *\)-algebras applicable to the \(L^ p\) spaces [Ann. Inst. Fourier 24(1974), No.4, 121-155 (1975; Zbl 0287.46078)].
bounded generator of a one-parameter group of positive operators on an ordered Banach space
order derivations on \(L^ p\)-spaces of \(W^ *\)- algebras
scientific article; zbMATH DE number 3996425
scientific article