Spectral Decompositions of Isometries on cp

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 cp, 1FpF`, is examined. The UMD structure, for 1-p-`, and triangular truncations and duality for ps1, ` 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