Isometries for unitarily invariant norms (Q1772720)

After a brief survey of results and proof techniques in the study of isometries for unitarily invariant norms on real and complex rectangular matrices, the paper presents a characterization of a class of linear isometries without the linearity assumption. Some related results and problems like the invariant norms on other matrix and operator algebras and spaces, and isometry problems without the surjectivity assumption are finally discussed.