@article {
author = {Khoddami, Ali Reza},
title = {Non-Equivalent Norms on $C^b(K)$},
journal = {Sahand Communications in Mathematical Analysis},
volume = {17},
number = {4},
pages = {1-11},
year = {2020},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2020.121559.748},
abstract = {Let $A$ be a non-zero normed vector space and let $K=\overline{B_1^{(0)}}$ be the closed unit ball of $A$. Also, let $\varphi$ be a non-zero element of $ A^*$ such that $\Vert \varphi \Vert\leq 1$. We first define a new norm $\Vert \cdot \Vert_\varphi$ on $C^b(K)$, that is a non-complete, non-algebraic norm and also non-equivalent to the norm $\Vert \cdot \Vert_\infty$. We next show that for $0\neq\psi\in A^*$ with $\Vert \psi \Vert\leq 1$, the two norms $\Vert \cdot \Vert_\varphi$ and $\Vert \cdot \Vert_\psi$ are equivalent if and only if $\varphi$ and $\psi$ are linearly dependent. Also by applying the norm $\Vert \cdot \Vert_\varphi $ and a new product `` $\cdot$ '' on $C^b(K)$, we present the normed algebra $ \left( C^{b\varphi}(K), \Vert \cdot \Vert_\varphi \right)$. Finally we investigate some relations between strongly zero-product preserving maps on $C^b(K)$ and $C^{b\varphi}(K)$.},
keywords = {Normed vector space,Equivalent norm,Zero-product preserving map,Strongly zero-product preserving map},
url = {https://scma.maragheh.ac.ir/article_44696.html},
eprint = {https://scma.maragheh.ac.ir/article_44696_f8ab5402f7af7d2d59f42fcd0b311ec3.pdf}
}