Single elements and module isomorphisms of some operator algebra modules

摘要

In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the Alg L-module uis initiated, where L is a completely distributive subspace lattice on a Hilbert space H Furthermore, as an application of single elements, we study module isomorphisms between norm closed Alg N -modules, where N is a nest, and obtain the following result: Suppose that U,V, are norm closed Alg N -modules and that φ: U→V is a module isomorphism. Then U=V and there exists a non-zero complex number λ such that φ (T)=λ(T) VT ∈U.