Completely Continuous Banach Algebras
عنوان مقاله: Completely Continuous Banach Algebras
شناسه ملی مقاله: JR_IJNAA-10-1_006
منتشر شده در در سال 1398
شناسه ملی مقاله: JR_IJNAA-10-1_006
منتشر شده در در سال 1398
مشخصات نویسندگان مقاله:
- - - Faculty of Mathematical Sciences, Malayer University, P. O. Box ۱۶۸۴۶-۱۳۱۱۴, Malayer, Iran
خلاصه مقاله:
- - - Faculty of Mathematical Sciences, Malayer University, P. O. Box ۱۶۸۴۶-۱۳۱۱۴, Malayer, Iran
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.
کلمات کلیدی: Amenability, Completely continuous, Banach algebra
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1561772/