Extending Representations of Dense Subalgebras of $C^{\star }$-Algebras, and Spectral Invariance

Larry B. Schweitzer

Let $A$ be a dense Fréchet subalgebra of the $C^{\star }$-algebra of compact operators $\mathcal{K}$ on a seprable Hilbert space. Assume that $A$ is spectral invariant in $\mathcal{K}$. We show…