Weak<IMG BORDER="0" SRC="/proc/2004-132-06/S0002-9939-04-07385-X/gif-title0/img1.gif" > properties of weighted convolution algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Weak properties of weighted convolution algebras

Authors:	Sandy Grabiner

Institution:	Department of Mathematics, Pomona College, Claremont, California 91711

Abstract:	Suppose that $L^{1}(\omega)$ is a weighted convolution algebra on $\mathbf{R}^{+}=0,\infty)$ with the weight $\omega (t)$ normalized so that the corresponding space $M(\omega)$ of measures is the dual space of the space $C_{0}(1/\omega)$ of continuous functions. Suppose that $\phi: L^{1}(\omega)\rightarrow \ensuremath{L^{1}(\omega')}$ is a continuous nonzero homomorphism, where $\ensuremath{L^{1}(\omega')}$ is also a convolution algebra. If $L^{1}(\omega)\ast f$ is norm dense in $L^{1}(\omega)$ , we show that $\ensuremath{L^{1}(\omega')}\ast\phi (f)$ is (relatively) weak $^{\ast}$ dense in $\ensuremath{L^{1}(\omega')}$ , and we identify the norm closure of $\ensuremath{L^{1}(\omega')}\ast\phi (f)$ with the convergence set for a particular semigroup. When $\phi$ is weak $^{\ast}$ continuous it is enough for $L^{1}(\omega)\ast f$ to be weak $^{\ast}$ dense in $L^{1}(\omega)$ . We also give sufficient conditions and characterizations of weak $^{\ast}$ continuity of $\phi$ . In addition, we show that, for all nonzero in $\ensuremath{L^{1}(\omega )}$ , the sequence $f^{n}/\vert\vert f^{n}\vert\vert$ converges weak $^{\ast}$ to 0. When $\omega$ is regulated, $f^{n+1}/\vert\vert f^{n}\vert\vert$ converges to 0 in norm.

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏