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Reflexivity of the translation-dilation algebras on L^2(R)

R. H. Levene·S. C. Power
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Abstract

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.

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R. H. Levene, S. C. Power. 2004-01-15. Reflexivity of the translation-dilation algebras on L^2(R). https://doi.org/10.1142/s0129167x03002125

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