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

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

2004-01-15

arxiv.org/abs/math/0401187v2

Mathematics

Functional Analysis

10 pages, no figures To appear in the International Journal of Mathematics

Scientific paper

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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