Cuntz-Krieger algebras for infinite matrices

Given an arbitrary infinite matrix A = {A(i,j)}(i, j is an element of G) wi th entries in {0, 1} and having no identically zero rows, we define an alge bra O-A as the universal C*-algebra generated by partial isometries subject to conditions that generalize, to the infinite case, those introduced by C untz and Krieger for finite matrices. We realize O-A as the crossed product algebra for a partial dynamical system and, based on this description, we extend to the infinite case some of the main results known to hold in the f inite case, namely the uniqueness theorem, the classification of ideals, an d the simplicity criteria. O-A is always nuclear and we obtain conditions f or it to be unital and purely infinite.