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The w*-closed triple semigroup algebra was introduced by Power and the authorin [19], where it was proved to be reflexive and to be chiral, in the sense ofnot being unitarily equivalent to its adjoint algebra. Here an analogousoperator norm-closed triple semigroup algebra $A_{ph}^{G+}$ is considered andshown to be a triple semi-crossed product for the action on analytic almostperiodic functions by the semigroups of one-sided translations and one-sideddilations. The structure of isometric automorphisms of $A_{ph}^{G+}$ isdetermined and $A_{ph}^{G+}$ is shown to be chiral with respect to isometricisomorphisms.

The norm closed triple semigroup algebra