Isometric representations of some quotients of H-infinity of an annulus

Let A denote an annulus, E a finite subset of A with at least three element s, and I-E the ideal of functions in H-infinity(A) which vanish at the poin ts of E. The quotient H-infinity(A)/I-E does not have a completely isometri c representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representat ion on a Hilbert space of dimension twice the cardinality of E.