Frobenius C*-algebras and local adjunctions of C*-correspondences

Generalizing the well-known correspondence between two-sided adjunctions and Frobenius algebras, we establish a one-to-one correspondence between local adjunctions of C*-correspondences, as defined and studied in prior work with Clare and Higson; and Frobenius C*-algebras, a natural C*-algebraic adaptation of the standard notion of Frobenius algebras that we introduce here.