TY - JOUR ID - 34113 TI - $(-1)$-Weak Amenability of Second Dual of Real Banach Algebras JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Alihoseini, Hamidreza AU - Alimohammadi, Davood AD - Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran. Y1 - 2018 PY - 2018 VL - 12 IS - 1 SP - 59 EP - 88 KW - Banach algebra‎ KW - ‎Banach module‎ KW - ‎Complexification‎ KW - ‎Derivation‎ KW - ‎$(-1)$-Weak amenability DO - 10.22130/scma.2018.88929.466 N2 - 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. UR - https://scma.maragheh.ac.ir/article_34113.html L1 - https://scma.maragheh.ac.ir/article_34113_087079dab0bf46a0162249a173f41f59.pdf ER -