Weak* properties of weighted convolution algebras II

Sandy Grabiner. "Weak* properties of weighted convolution algebras II." Studia Mathematica 198.1 (2010): 53-67. <http://eudml.org/doc/285841>.

@article{SandyGrabiner2010,
abstract = {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.},
author = {Sandy Grabiner},
journal = {Studia Mathematica},
keywords = {weighted convolution algebra; continuous semigroup; dense ideal; algebra weight},
language = {eng},
number = {1},
pages = {53-67},
title = {Weak* properties of weighted convolution algebras II},
url = {http://eudml.org/doc/285841},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Sandy Grabiner
TI - Weak* properties of weighted convolution algebras II
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 1
SP - 53
EP - 67
AB - 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.
LA - eng
KW - weighted convolution algebra; continuous semigroup; dense ideal; algebra weight
UR - http://eudml.org/doc/285841
ER -