Frame-Less Hilbert C*-Modules

We show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A 1 -module admitting no frames, where A 1 is the unitization of A . In particular, there exists a frame-less Hilbert C*-module over the C*-algebra K(²) CI² .