Abstract
Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.
Highlights
Introduction andPreliminaries http://creativecommons.org/licenses/by/4.0/ Open AccessKadison and Kastler in [1] initiated the study of uniform perturbations of operator algebras
We consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras
We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm
Summary
Introduction andPreliminaries http://creativecommons.org/licenses/by/4.0/ Open AccessKadison and Kastler in [1] initiated the study of uniform perturbations of operator algebras. Perturbation problem of operator algebras was first introduced by Kadison and Kastler. We consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm. Kadison and Kastler in [1] initiated the study of uniform perturbations of operator algebras.
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