Operators on locally Hilbert space
The authors study the pro-\(C^*\)-algebra \(L(H)\) defined on a locally Hilbert space \(H\). Utilizing the Arens-Michael decomposition, they decompose the operators in \(L(H)\) and try to repair a gap found in the Arens-Michael decomposition of \(L(H)\) in [Topological algebras with involution. Amsterdam: Elsevier/North-Holland (2005; Zbl 1197.46001), Remarks (i), pp. 107--108] by \textit{M. Fragoulopoulou}. They also investigate the algebra \(K(H)\) of compact operators. The rank one operators and minimal projections in the setup of locally Hilbert spaces are also studied. They obtain the polar decomposition of an operator in \(L(H)\) by exploiting the inverse limit system. Finally, they introduce the Schatten class operators including the trace class operators and the Hilbert-Schmidt operators.
scientific article; zbMATH DE number 6651351