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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.3 Antofagasta Dec. 2007

http://dx.doi.org/10.4067/S0716-09172007000300003 

 

Proyecciones Journal of Mathematics
Vol. 26, Nº 3, pp. 253-257, December 2007.
Universidad Católica del Norte
Antofagasta - Chile


QUASI - MACKEY TOPOLOGY


SURJIT SINGH KHURANA
University of Iowa, U. S. A.

Correspondencia a:



Abstract
Let E1, E2 be Hausdorff locally convex spaces with E2 quasi-complete, and T : E1 → E2 a continuous linear map. Then T maps bounded sets of E1 into relatively weakly compact subsets of E2 if and only if T is continuous with quasi-Mackey topology on E1. If E1 has quasi-Mackey topology and E2 is quasi-complete, then a sequentially continuos linear map T : E1 → E2 is an unconditionally converging operator.


Key words : quasi - Mackey topology, weakly unconditionally Cauchy, unconditionally converging operators.
Subjclass 2000 : Primary: 46A05, 46A20; Secondary: 46A50.

REFERENCES
[1] Diestel, J., Uhl, J. J., Vector Measures, Amer. Math. Soc. Surveys, Vol. 15, Amer. Math. Soc., (1977).
[2] Howard Joe, Unconditionally converging operators in locally convex spaces, Comment. Math. Univ. Carolinae, 13, pp. 637-641, (1972).
[3] Qiu, Jinghui, Local completeness and dual local quasi-completeness. Proc. Amer. Math. Soc. 129, pp. 1419—1425, (2001).
[4] Peralta, Antonio M., Villanueva, Ignacio, Wright, J. D. Maitland, Ylinen, Kari, Topological characterisation of weakly compact operators, J. Math. Anal. Appl. 325, pp. 968—974, (2007).
[5] Schaefer, H. H., Topological Vector spaces, Springer Verlag, (1986).

SURJIT SINGH KHURANA
Department of Mathematics
University of Iowa
Iowa City
Iowa 52242
U. S. A.
e-mail : mailto:khurana@math.uiowa.edu

Received : July 2007. Accepted : October 2007

 

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