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Throughout this chapter 0 0] denotes a unital C*-algebra and τ a locally convex topology on 0. Let 0[τ] denote the completion of 0 with respect to the topology τ. Under certain conditions on τ, a subspace of 0[τ], containing 0, will form (together with 0) a locally convex quasi *-algebra ([τ], 0), which is named locally convex quasi C*-algebra. Examples and basic properties of such algebras are presented. So, let 0[0] and τ be as before, with pλλ Λ a defining family of seminorms for τ. Suppose that τ satisfies the properties: (T1)0[ τ] is a locally convex *-algebra with separately continuous multiplication.(T2)τ 0. © 2020, Springer Nature Switzerland AG. |
