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.