Existence of $E_0$--Semigroups for Arveson Systems: Making Two Proofs into One

Since quite a time there were available only two rather difficult and involved proofs, the original one by Arveson and a more recent one by Liebscher, of the fact that for every Arveson system there exists an E_0-semigroup. We put together two recent short proofs, one by Skeide and one by Arveson, to obtain a still simpler one, which unfies the advantages of each proof and discards with their disadvantages.