Topological characterisation of weakly compact operators

Antonio M. Peralta, Ignacio Villanueva, John David Maitland Wright, Kari Ylinen

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Let X be a Banach space. Then there is a locally convex topology for X, 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. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)968-974
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume325
Issue number2
Early online date23 Mar 2006
DOIs
Publication statusPublished - 15 Jan 2007

Keywords

  • weakly compact operators
  • right topology
  • Mackey topology

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