Niels Laustsen, University of Lancaster

$K$-theory for Banach sequence algebras

Let $\mathcal{A}$ be a Banach algebra which contains the algebra~$c_{00}$ of
finitely supported, complex-valued sequences as a dense subalgebra, and suppose
that the canonical basis for $c_{00}$ is a Schauder basis for~$\mathcal{A}$.
Then $K_0(\mathcal{A})$ is isomorphic to the additive group
$\mathbb{Z}^{<\infty}$ of finitely supported, integer-valued sequences, while
$K_1(\mathcal{A}) = \{0\}$.