Biblioteca de la Universidad Complutense de Madrid

Topological characterisation of weakly compact operators

Impacto



Peralta Pereira, Antonio Miguel y Villanueva, Ignacio y Wright, J. D. Maitland y 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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URL Oficial: http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/



Resumen

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).


Tipo de documento:Artículo
Palabras clave:Weakly compact operators; Right topology; Mackey topology
Materias:Ciencias > Matemáticas > Topología
Código ID:14530
Referencias:

[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.

Depositado:07 Feb 2012 08:29
Última Modificación:13 Dic 2013 17:38

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