2024 : 6 : 15
Davood Alimohammadi

Davood Alimohammadi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-9398-6213
Education: PhD.
ScopusId: 6505995626
Faculty: Science
Address: Arak University
Phone:

Research

Title
Weak Amenability of Second Dual of Real Banach Algebras-
Type
JournalPaper
Keywords
Banach algebra‎, ‎Banach module‎, ‎Complexification‎, ‎Derivation‎, ‎$(-1)$-Weak amenability.d
Year
2019
Journal Sahand Communications in Mathematical Analysis
DOI
Researchers Davood Alimohammadi ، Hamidreza Alihoseini

Abstract

‎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.d