Isometries of Haagerup--Schultz algebras

Abstract

We establish a version of the classical results concerning descriptions of isometries on $C^*$-algebras and noncommutative $L_p$-spaces due to Kadison (1951) and Yeadon (1981) in the setting of Haagerup--Schultz algebras. Precisely, we show that (not necessarily surjective) isometries on such algebras are necessarily implemented by partial isometries and trace-preserving Jordan $^*$-monomorphisms.