The spectral radius in \(\mathcal{C}_0(X)\)-Banach algebras (Q1946283)

The author proves that there exists an isometric isomorphism between a fiber of a monotone completion \({\mathcal H}(Y, EX)\) and a monotone completion \({\mathcal H}(Y, E)\), where \(E\) is an upper semicontinuous field of Banach spaces over a locally compact Hausdorff space \(Y\) and \(X\) is a second countable locally compact Hausdorff space. It gives a possibility to carry out some \(K\)-theoretical calculations fiberwise.