Topological characterization of weakly compact operators revisited
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Autores: Antonio Miguel Peralta Pereira
- Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 22, Nº 2, 2007 (Ejemplar dedicado a: Banach space theory: classical topics and new directions. Cáceres 2006), págs. 215-223
- Idioma: inglés
- Enlaces
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Resumen
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.
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