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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 | ||
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