An extension of the notion of a C*-algebra to unbounded operators. In complete analogy to abstract and concrete definitions of a C*-algebra, there are abstract and concrete definitions of an extended C*-algebra. An extended C*-algebra is a complex (or real) locally convex *-algebra such that the poset of subsets that are closed, absolutely convex, bounded, , and has a maximal element ; is pseudocomplete: for every as above, the Minkowski functional of induces a complete norm on ; is symmetric:...