The norm closed triple semigroup algebra

Abstract

The w*-closed triple semigroup algebra was introduced by Power and the author in [21], where it was proved to be reflexive and to be chiral, in the sense of not being unitarily equivalent to its adjoint algebra. Here an analogous operator norm-closed triple semigroup algebra \(A_{ph}^{G^+}\) is considered and shown to be a triple semi-crossed product for the action on analytic almost periodic functions by the semigroups of one-sided translations and one-sided dilations. The structure of isometric automorphisms of \(A_{ph}^{G^+}\) is determined and \(A_{ph}^{G^+}\) is shown to be chiral with respect to isometric isomorphisms.

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Kastis, E. The norm closed triple semigroup algebra. Isr. J. Math. 230, 855–894 (2019). https://doi.org/10.1007/s11856-019-1839-9

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