2026/07/29 by Kai Fang, Jinghao Huang, Karimbergen Kudaybergenov +1
Mathematics · #math.FA
arxiv created 2026/07/29 · arxiv updated 2026/07/30
Let E(M,τ) and F(M,τ) be two Calkin operator spaces affiliated with a semifinite von Neumann algebra M equipped with a semifinite faithful normal trace τ. We show that if M is atomless, τ is finite, and E(v,τ)\not⊆ F(M,τ), then every order-measure continuous and disjointness-preserving mapping T:E(M,τ)\xrightarrow\rm into F(M,τ) is identical to the zero mapping, which establishes a noncommutative version of Abramovich's theorem. We also show that every positive isometry T from a normed M-bimodule E(M,τ) of τ-measurable operators into another F(M,τ) preserves disjointness provided that the norm of F(M,τ) is strictly monotone. As an application, we obtain the general form of T, which extends and unifies several results due to Abramovich, de Jager, Conradie, Veksler and Sukochev et al. \citeSV,HSZ20,Abra1991,vek,dC20.