Isometries between C$^*$-algebras with finite corank

We give a characterization of linear isometries with finite corank between two arbitrary unital C$^*$-algebras in terms of Jordan $^*$-homomorphisms and ``finite-dimensional remainders''.

Also, the corresponding results are given for linear isometries and linear order embeddings between self-adjoint parts of C$^*$-algebras.

In the finite-dimensional case, we give new examples of linear isometries between matrix algebras.