Reflexivity of the translation-dilation algebras on L^2(R)
Functional Analysis
2015-02-06 v2 Operator Algebras
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.
Keywords
Cite
@article{arxiv.math/0401187,
title = {Reflexivity of the translation-dilation algebras on L^2(R)},
author = {R. H. Levene and S. C. Power},
journal= {arXiv preprint arXiv:math/0401187},
year = {2015}
}
Comments
10 pages, no figures To appear in the International Journal of Mathematics