Abstract
Suppose $ A$ is a Banach algebra and $\epsilon$ is in A with $\|\epsilon\|\leq 1$. In this note we aim to study the algebraic properties of the Banach algebra $ A_\epsilon$, where the product on $ A_\epsilon$ is given by $a \odot b = a \epsilon b$, for $a, b \in A$. In particular we study the Arens regularity, amenability and derivations on $ A_\epsilon$. Also we prove that if $ A$ has an involution then $ A_\epsilon$ has the same involution just when $\epsilon = 1$ or $-1$.
Citation
R. A. Kamyabi-Gol. M. Janfada. "BANACH ALGEBRAS RELATED TO THE ELEMENTS OF THE UNIT BALL OF A BANACH ALGEBRA." Taiwanese J. Math. 12 (7) 1769 - 1779, 2008. https://doi.org/10.11650/twjm/1500405087
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