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Title: Topological characterization of weakly compact operators revisited
Authors: Peralta, Antonio M.
Keywords: Operador débilmente compacto;Topología derecha;Topología Mackey;Propiedad (V);Weakly compact operator;Right topology;Mackey topology;Property (V)
Issue Date: 2007
Publisher: Universidad de Extremadura, Servicio de Publicaciones
Abstract: In this note we revise and survey some recent results established in [8]. We shall show that for each Banach space 𝑋, there exists a locally convex topology for 𝑋, termed the “Right Topology”, such that a linear map 𝑇, from 𝑋 into a Banach space 𝑌, is weakly compact, precisely when 𝑇 is a continuous map from 𝑋, equipped with the “Right” topology, into 𝑌 equipped with the norm topology. We provide here a new and shorter proof of this result. We shall also survey the results concerning sequentially Right-to-norm continuous operators.
ISSN: 0213-8743
Appears in Collections:Extracta Mathematicae Vol. 22, nº 2 (2007)

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