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A locally convex quasi *-algebra is a pair consisting of a locally convex space [τ] containing densely a *-algebra 0, whose multiplication and involution extend to, in the sense that for any a and x 0, the elements ax, xa belong to, in such a way that (ax)* = x*a*, (xa)* = a*x* and moreover the left and right multiplications of the elements of by a fixed x0, as well as the involution on [τ] are continuous. A typical example is obtained by taking as the completion of a locally convex *-algebra 0[τ] with continuous involution and separately continuous multiplication. © 2020, Springer Nature Switzerland AG. |