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Satellite conference on Banach spaces · ICM2006 Topological characterization of weakly compact operators revisited †

By Antonio M. Peralta


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

Topics: Key words, Weakly compact operator, Right topology, Mackey topology, Property (V) AMS Subject Class. (2000, 47B07, 47A20
Year: 2006
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