On countable codimensional subspaces in ultra-(DF) spaces. (English) Zbl 0597.46004
It is proved that a countable codimensional subspace G of an Ultra-(DF) space E is an Ultra-(DF) space provided G has property (b), i.e. for every bounded subset B of E the codimension of G in the linear span of \(G\cup B\) is finite. Moreover, the property of being Ultra-(DF) is also maintained in subspaces of countable codimension, if the initial Ultra- (DF) space is sequentially complete and boundedly summing, or an ultrabarrelled space.
MSC:
46A04 | Locally convex Fréchet spaces and (DF)-spaces |
Keywords:
countable codimensional subspace; Ultra-(DF) space; subspaces of countable codimension; ultrabarrelled spaceReferences:
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