Continuity of operator-valued functions in the \(*\)-algebra of locally measurable operators. (English) Zbl 1313.46066

Let \(M\) be a von Neumann algebra, \(LS(M)\) be the \(*\)-algebra of all locally measurable operators affiliated to \(M\), with the local measure topology; see [F. J. Yeadon, Proc. Camb. Philos. Soc. 74, 257–268 (1973; Zbl 0272.46043)]. The authors find sufficient conditions for the continuity of the mapping \(T\mapsto f(T)\), \(T\in LS(M)\), where \(f\) is a complex-valued function on \(\mathbb R\).


46L51 Noncommutative measure and integration
46H35 Topological algebras of operators
47L60 Algebras of unbounded operators; partial algebras of operators


Zbl 0272.46043