Topological characterisation of weakly compact operators

Peralta Pereira, Antonio Miguel; Villanueva Díez, Ignacio; Wright, J. D. Maitland; Ylinen, Kari

Topological characterisation of weakly compact operators

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Official URL

https//doi.org/10.1016/j.jmaa.2006.02.066

Publication date

2007

Authors

Peralta Pereira, Antonio Miguel

Villanueva Díez, Ignacio

Wright, J. D. Maitland

Ylinen, Kari

Publisher

Elsevier

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URI

https://hdl.handle.net/20.500.14352/49796

Citation

Peralta Pereira, A. M., Villanueva Díez, I., Wright, J. D. M. & Ylinen, K. «Topological Characterisation of Weakly Compact Operators». Journal of Mathematical Analysis and Applications, vol. 325, n.o 2, enero de 2007, pp. 968-74. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2006.02.066.

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).