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

被引：2

作者：

Bonet, J ^{[1
]}

Conejero, JA

机构：

[1] Univ Politecn Valencia, Dept Matemat Aplicada, ETS Arquitectura, E-46071 Valencia, Spain

[2] Univ Politecn Valencia, Dept Matemat Aplicada, Fac Informat, E-46071 Valencia, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 12期

关键词：

bounded below operators; monomorphisms; almost open operators; locally convex spaces; quasinormable spaces;

D O I：

10.1090/S0002-9939-01-06248-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3683 / 3690

页数：8

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