Spectral decompositions of isometries on c(p)

The spatial action of the Stone-type spectral family for a certain type of strongly continuous one-parameter groups of surjective isometries, as well as of the spectral decomposition of their single elements on c(p), 1 less than or equal to p less than or equal to infinity, is examined. The UMD structure, for 1 < p < infinity, and triangular truncations and duality for p = 1, infinity are involved. In various cases, concrete descriptions of the associated Riesz-Nagy operators and Arveson's spectral subspaces are derived as byproducts of independent interest. (C) 1997 Academic Press.