Taggart, Robert2015-12-070025-5874http://hdl.handle.net/1885/28323Suppose that {Tt : t ≥ 0} is a symmetric diffusion semigroup on L 2(X) and denote by T̃t:t ≥ 0 its tensor product extension to the Bochner space Lp(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the200910.1007/s00209-008-0360-32015-12-07