×

zbMATH — the first resource for mathematics

On the existence of the continuous right-inverse for an operator in a class of locally convex spaces. (Russian) Zbl 0751.46008
The author proves that a continuous linear operator from an \(LN^*\) space to another such space has a continuous right-inverse (perhaps nonlinear) operator — Michael’s theorem for non-metrizable spaces.

MSC:
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
54E99 Topological spaces with richer structures
47J05 Equations involving nonlinear operators (general)
PDF BibTeX XML Cite