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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Official URL: http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/

## 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).

Item Type: | Article |
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Uncontrolled Keywords: | Weakly compact operators; Right topology; Mackey topology |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 14530 |

References: | [1] Ch.-H. Chu, P. Mellan, JB *-triples have Pelczynski's Property V, Manuscripta Math. 93 (3) (1997) 337-347. [2] J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math., vol. 92, Springer, New York, 1984. [3] N. Dunford, J.T. Schwartz, Linear Operators (vol. I), Interscience, New York, 1967. [4] G. Kothe, Topological VectorSpaces, Springer, 1969. [5] J. Qiu, Local completeness and dual local quasi-completeness, Proc. Amer. Math. Soco 129 (2000) 1419-1425. [6] A.P. Robertson, W.J. Robertson, Topological Vector Spaces, Cambridge University Press, 1973. [7] M. Takesaki, 1beory of Operator Algebras 1, Springer, New York, 1979. [8] J.D.M. Wright, K. Ylinen, Multilinear maps on products of operator algebras, J. Math. Anal. Appl. 292 (2004) 558- 570. |

Deposited On: | 07 Feb 2012 08:29 |

Last Modified: | 13 Dec 2013 17:38 |

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