Quasi - mackey topology

Authors

  • Surjit Singh Khurana University of Iowa, U. S. A.

DOI:

https://doi.org/10.4067/S0716-09172007000300003

Keywords:

quasi - Mackey topology, Weakly unconditionally Cauchy, Unconditionally converging operators.

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 continuous linear map T : E1 → E2 is an unconditionally converging operator.

Author Biography

Surjit Singh Khurana, University of Iowa, U. S. A.

Department of Mathematics.

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).

Published

2017-04-12

How to Cite

[1]
S. S. Khurana, “Quasi - mackey topology”, Proyecciones (Antofagasta, On line), vol. 26, no. 3, pp. 253-257, Apr. 2017.

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