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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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Additional Information

José Bonet
Affiliation: Departamento de Matemática Aplicada, ETS Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
Email: jbonet@mat.upv.es

José A. Conejero
Affiliation: Departamento de Matemática Aplicada, Fac. Informatica, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
Email: aconejero@mat.upv.es

DOI: https://doi.org/10.1090/S0002-9939-01-06248-7
Keywords: Bounded below operators, monomorphisms, almost open operators, locally convex spaces, quasinormable spaces
Received by editor(s): May 2, 2000
Published electronically: June 27, 2001
Additional Notes: The authors were partially supported by the project DGESIC, PB97-0333.
The second author was also supported by the Universidad Politécnica de Valencia, grant 19980998.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society