On \(K\)-groups of operator algebra on the 1-shift space (Q953230)

Their main result is to show that the \(K\)-theory groups \(K_0\) and \(K_1\) for the Banach algebra \(B(X_{GM2})\) of all bounded linear operators on the \(1\)-shift space \(X_{GM2}\) of \textit{W. T. Gowers} and \textit{B. Maurey} [Math. Ann. 307, No.~4, 543--568 (1997; Zbl 0876.46006)] are \(\mathbb Z\) and zero, respectively. For its proof, the six-term exact sequence of \(K\)-groups for a short exact sequence of \(B(X_{GM2})\) is computed explicitly, and for this, the \(K\)-groups of the Wiener algebra are also computed, and their generators are determined explicitly as well, and a characterization of Fredholm operators in \(B(X_{GM2})\) is also obtained.