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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
Arens regularity of real Banach algebras and $(-1)$-weak amenability of second dual of real Banach algebras
Type
Presentation
Keywords
Banach algebra‎, ‎Banach module‎, ‎Complexification‎, ‎Derivation‎, ‎$(-1)$-Weak amenability
Year
2019
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$‎. ‎We first show that ‎$ A $ is Arens regular if and only if ‎$ A_{‎\mathbb{C}‎} $ is Arens regular. Next we prove that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_\mathbb{C})^* $ is a complex Banach $ (A_\mathbb{C})^{**}$-module‎. ‎Finally, we show that $ A^{**} $ is $ (-1)$-weakly amenable if and only if $ (A_\mathbb{C})^{**} $ is $ (-1)$-weakly amenable‎. d