On Well-behaved Unbounded Representations of *-Algebras

Abstract

A general approach to the well-behaved unbounded *-representations of a *-algebra X is proposed. Let B be a normed *-algebra equipped with a left action |> of X on B such that (x |> a)^+ b=a^+(x^+ |> b) for a,b\in B and x\in X. Then the pair (X,B) is called a compatible pair. For any continuous non-degenerate *-representation ρof B there exists a closed *-representation ρ' of X such that ρ'(x)ρ(b)=ρ(x |> b), where x\in X and b\in B. The *-representations ρ' are called the well-behaved *-representations associated with the compatible pair (X,B). A number of examples are developed in detail.

16 pages

References in corpus (1)

• Algebras of distributions suitable for phase-space quantum mechanics. I

Cited by in corpus (5)

• Invariant integration theory on non-compact quantum spaces: Quantum (n,1)-matrix ball
• Integrable representations of involutive algebras and Ore localization
• An operator-theoretic approach to invariant integrals on quantum homogeneous sl_{n+1}(R)-spaces
• Hilbert space representations of cross product algebras II
• Bounded elements in certain topological partial *-algebras