Linear maps preserving invertibility or related spectral properties
The authors survey some recent results about linear maps on operator algebras that preserve invertibility. They also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. Moreover, they present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, they give a negative answer to a problem posed by Gao and Hou on characterizing spectrum preserving elementary operators. Several open problems are also mentioned.
scientific article; zbMATH DE number 2002320
scientific article