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The sets of monomorphisms and of almost open operators between locally convex spaces |
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| Authors: | José Bonet José A Conejero |
| Institution: | Departamento de Matemática Aplicada, ETS Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain ; Departamento de Matemática Aplicada, Fac. Informatica, Universidad Politécnica de Valencia, E-46071 Valencia, Spain |
| 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. |
| Keywords: | Bounded below operators monomorphisms almost open operators locally convex spaces quasinormable spaces |
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