We show that if ϕ is a continuous homomorphism between weighted convolution algebras on ℝ⁺, then its extension to the corresponding measure algebras is always weak* continuous. A key step in the proof is showing that our earlier result that normalized powers of functions in a convolution algebra on ℝ⁺ go to zero weak* is also true for most measures in the corresponding measure algebra. For some algebras, we can determine precisely which measures have normalized powers converging to zero weak*. We also include a variety of applications of weak* results, mostly to norm results on ideals and on convergence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-3,
author = {Sandy Grabiner},
title = {Weak* properties of weighted convolution algebras II},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {53-67},
zbl = {1204.43004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-3}
}
Sandy Grabiner. Weak* properties of weighted convolution algebras II. Studia Mathematica, Tome 196 (2010) pp. 53-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-3/