Volume 3, Issue 2 (12-2022)
MACO 2022, 3(2): 17-24 |
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Taghavi A. Topological and Banach Space interpretation for real sequences whose consecutive terms have a bounded difference. MACO 2022; 3 (2) : 3
URL: http://maco.lu.ac.ir/article-1-113-en.html
URL: http://maco.lu.ac.ir/article-1-113-en.html
Abstract: (1190 Views)
In this paper we give a topology-dynamical interpretation for the space of all integer sequences $P_n$ whose consecutive difference $P_{n+1}-P_n$ is a bounded sequence. We also introduce a new concept textit{"Rigid Banach space"}. A rigid Banach space is a Banach space $X$ such that for every continuous linear injection $j:Xto X,;overline{J(X)}$ is either isomorphic to $X$ or it does not contain any isometric copy of $X$. We prove that $ell_{infty}$ is not a rigid Banach space. We also discuss about rigidity of Banach algebras.
Article number: 3
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