پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 678 |
| تعداد مقالات | 9,888 |
| تعداد مشاهده مقاله | 70,059,321 |
| تعداد دریافت فایل اصل مقاله | 49,331,646 |
Completely continuous Banach algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 7، شماره 1، فروردین 2016، صفحه 301-308 اصل مقاله (343.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2016.383 | ||
| نویسنده | ||
| Bahman Hayati | ||
| Department of Mathematics, Malayer University, P.O. Box 16846-13114, Malayer, Iran | ||
| تاریخ دریافت: 28 فروردین 1394، تاریخ بازنگری: 22 آذر 1394، تاریخ پذیرش: 05 دی 1394 | ||
| چکیده | ||
| For a Banach algebra $\mathfrak{A}$, we introduce ~$c.c(\mathfrak{A})$, the set of all $\phi\in \mathfrak{A}^*$ such that $\theta_\phi:\mathfrak{A}\to \mathfrak{A}^*$ is a completely continuous operator, where $\theta_\phi$ is defined by $\theta_\phi(a)=a\cdot\phi$~~ for all $a\in \mathfrak{A}$. We call $\mathfrak{A}$, a completely continuous Banach algebra if $c.c(\mathfrak{A})=\mathfrak{A}^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an open problem raised for the first time by J.E Gale, T.J. Ransford and M. C. White: Is there exist an infinite dimensional amenable Banach algebra whose underlying Banach space is reflexive? We prove that a reflexive, amenable, completely continuous Banach algebra with the approximation property is trivial. | ||
| کلیدواژهها | ||
| Amenability؛ Completely continuous؛ Banach algebra | ||
|
آمار تعداد مشاهده مقاله: 17,159 تعداد دریافت فایل اصل مقاله: 11,364 |
||