  A full set of Casimir operators for the Lie superalgebra $gl(m/\infty)$ is
constructed and shown to be well defined in the category $O_{FS}$ generated by
the highest weight irreducible representations with only a finite number of
non-zero weight components. The eigenvalues of these Casimir operators are
determined explicitly in terms of the highest weight. Characteristic identities
satisfied by certain (infinite) matrices with entries from $gl(m/\infty)$ are
also determined.
