2004/05/28 by W. Timmermann, Werner Timmermann, Timmermann, W. · 1 citation
Computer Science · Mathematics · #47L60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.OA #msc:47L60
paper · pdf · doi:10.48550/arxiv.math/0405545
7 pages The first version of the paper is replaced by this one, because in the first version the enumeration of the Theorems, Lemmas etc. were incorrect
openalex publication_date 2004/05/28 · arxiv created 2005/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal D be a dense linear manifold in a Hilbert space \mathcal H and let L+(\mathcal D) be the *-algebra of all linear operators A such that A \mathcal D ⊂ \mathcal D, A^* \mathcal D ⊂ \mathcal D. Denote by F(\mathcal D) the *-ideal of L+(\mathcal D) consisting of all finite-rank operators. A characterization of the structure of additive mappings of F(\mathcal D) preserving operators of rank one or projections of rank one is given. The corresponding results for algebras of bounded operators on Banach spaces were given by P. uSemrl.