Abstract
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 oncp, 1≤p≤∞, is examined. The UMD structure, for 1<p<∞, and triangular truncations and duality forp=1, ∞ 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.
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