The sets of monomorphisms and of almost open operators between locally convex spaces

Bonet, José; Conejero, José

doi:10.1090/S0002-9939-01-06248-7

The sets of monomorphisms and of almost open operators between locally convex spaces

Authors: José Bonet and José A. Conejero
Journal: Proc. Amer. Math. Soc. 129 (2001), 3683-3690
MSC (2000): Primary 46A32, 46A03, 46H35, 47A05, 47L05
DOI: https://doi.org/10.1090/S0002-9939-01-06248-7
Published electronically: June 27, 2001
MathSciNet review: 1860503
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Abstract:

If the set of monomorphisms between locally convex spaces is not empty, then it is an open subset of the space of all continuous and linear operators endowed with the topology of the uniform convergence on the bounded sets if and only if the domain space is normable. The corresponding characterization for the set of almost open operators is also obtained; it is related to the lifting of bounded sets and to the quasinormability of the domain space. Other properties and examples are analyzed.

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