Peralta Pereira, Antonio Miguel and Villanueva Díez, 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 |
|---|---|
| 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 09:29 |
| Last Modified: | 07 Feb 2012 09:29 |
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