2 00 9 Some classes of topological quasi ∗ - algebras
نویسنده
چکیده
The completion A[τ ] of a locally convex ∗-algebra A[τ ] with not jointly continuous multiplication is a ∗-vector space with partial multiplication xy defined only for x or y ∈ A0, and it is called a topological quasi ∗-algebra. In this paper two classes of topological quasi ∗-algebras called strict CQ-algebras and HCQ-algebras are studied. Roughly speaking, a strict CQ-algebra (resp. HCQ-algebra) is a Banach (resp. Hilbert) quasi ∗-algebra containing a C-algebra endowed with another involution # and C-norm ‖ ‖#. HCQ -algebras are closely related to left Hilbert algebras. We shall show that a Hilbert space is a HCQ-algebra if and only if it contains a left Hilbert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ-algebra is embedded in a HCQ-algebra.
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