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Topological characterisation of weakly compact operators


Peralta Pereira, Antonio Miguel and Villanueva, Ignacio and Wright, J. D. Maitland and Ylinen, Kari (2007) Topological characterisation of weakly compact operators. Journal of Mathematical Analysis and Applications, 325 (2). pp. 968-974. ISSN 0022-247X

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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).

Item Type:Article
Uncontrolled Keywords:Weakly compact operators; Right topology; Mackey topology
Subjects:Sciences > Mathematics > Topology
ID Code:14530

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