$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
عنوان مقاله: $(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
شناسه ملی مقاله: JR_SCMA-12-1_005
منتشر شده در شماره 1 دوره 12 فصل در سال 1397
شناسه ملی مقاله: JR_SCMA-12-1_005
منتشر شده در شماره 1 دوره 12 فصل در سال 1397
مشخصات نویسندگان مقاله:
Hamidreza Alihoseini - Department of Mathematics, Faculty of Science, University of Arak, ۳۸۱۵۶-۸-۸۳۴۹, Arak, Iran.
Davood Alimohammadi - Department of Mathematics, Faculty of Science, University of Arak, ۳۸۱۵۶-۸-۸۳۴۹, Arak, Iran.
خلاصه مقاله:
Hamidreza Alihoseini - Department of Mathematics, Faculty of Science, University of Arak, ۳۸۱۵۶-۸-۸۳۴۹, Arak, Iran.
Davood Alimohammadi - Department of Mathematics, Faculty of Science, University of Arak, ۳۸۱۵۶-۸-۸۳۴۹, Arak, Iran.
Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{**}$-module. Next we prove that $ A^{**} $ is $ (-1)$-weakly amenable if and only if $ (A_mathbb{C})^{**} $ is $ (-1)$-weakly amenable. Finally, we give some examples of real Banach algebras which their second duals of some them are and of others are not $ (-1)$-weakly amenable.
کلمات کلیدی: Banach algebra, Banach module, Complexification, Derivation, $(-1)$-Weak amenability
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/892050/