کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6419055 | 1339370 | 2013 | 13 صفحه PDF | دانلود رایگان |
Let Ï be a continuous weight on R+ and let L1(Ï) be the corresponding convolution algebra. By results of Grønbæk and Bade & Dales the continuous derivations from L1(Ï) to its dual space Lâ(1/Ï) are exactly the maps of the form (DÏf)(t)=â«0âf(s)st+sÏ(t+s)ds(tâR+ and fâL1(Ï)) for some ÏâLâ(1/Ï). Also, every DÏ has a unique extension to a continuous derivation D¯Ï:M(Ï)âLâ(1/Ï) from the corresponding measure algebra. We show that a certain condition on Ï implies that DÂ¯Ï is weak-star continuous. The condition holds for instance if ÏâL0â(1/Ï). We also provide examples of functions Ï for which DÂ¯Ï is not weak-star continuous. Similarly, we show that DÏ and DÂ¯Ï are compact under certain conditions on Ï. For instance this holds if ÏâC0(1/Ï) with Ï(0)=0. Finally, we give various examples of functions Ï for which DÏ and DÂ¯Ï are not compact.
Journal: Journal of Mathematical Analysis and Applications - Volume 397, Issue 1, 1 January 2013, Pages 402-414