TOPOLOGICAL AND BANACH SPACE INTERPRETATION FOR REAL SEQUENCES WHOSE CONSECUTIVE TERMS HAVE A BOUNDED DIFFERENCE

Document Type : Original Article

Author
Ali Taghavi
Department of mathematics, Qom University of Technology, Qom, Iran
10.22034/maco.3.2.3
Abstract
In this paper we give a topology-dynamical interpretation for the space of all integer sequences Pn whose consecutive difference Pn+1 − Pn is a bounded sequence. We also introduce a new concept ”Rigid Banach space”. A rigid Banach space is a Banach space X such that for every continuous linear injection j : X → X, J(X) is either isomorphic to X or it does not contain any isometric copy of X. We prove that ℓ∞ is not a rigid Banach space. We also discuss about rigidity of Banach algebras.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 3, Issue 2
December 2022
Pages 17-24