We study positive representations through structures called crossed products of Banach algebras. These structures are inspired by group C*-algebras and crossed products of C*-algebras. During the... Show moreWe study positive representations through structures called crossed products of Banach algebras. These structures are inspired by group C*-algebras and crossed products of C*-algebras. During the course of the investigation a number of fundamental questions concerning general ordered Banach spaces also reared their head, and also warranted research. Show less