Banach spaces whose algebra of bounded operators has the integers as their $K_0$-group

Tomasz Kania, Piotr Koszmider, Niels Jakob Laustsen

Let $X$ and $Y$ be Banach spaces such that the ideal of operators which factor through $Y$ has codimension one in the Banach algebra $\mathcal{B}(X)$ of all bounded operators on $X…