  Let $A$ be a dense Fr\'echet subalgebra of the $C^\star$-algebra of compact
operators $\cal K$ on a seprable Hilbert space. Assume that $A$ is spectral
invariant in $\cal K$. We show that every algebraically cyclic
subrepresentation of a topologically irreducible representation of $A$ is
contained in a $\cal K$-module.
