Unbounded Induced *-Representations

In the first part we introduce conditional expectations of a *-algebra A onto a *-subalgebra B and use it to define the induction procedure for *-representations. Further we define the category of well-behaved *-representations for a class of group graded *-algebras and develope the Mackey theory in this category. The theory applies to a large variety of examples: Weyl algebra, q-deformed enveloping algebras u_q(su(2)), u_q(su(1,1)), the Virasoro algebra, *-algebras generated by dynamical systems etc.