Fr�chet Schwartz spaces and approximation properties
Copyright policy )Fr�chet Schwartz spaces and approximation properties
We show that there is a Fréchet Schwartz space with the approximation property which cannot be written as a reduced projective limit of Banach spaces with approximable linking maps. This also yields the first example of a complete locally convex space with the approximation property which is not a reduced projective limit of Banach spaces with the approximation property and thus gives a negative answer to an old problem [see also \textit{M. S. Ramanujan}, p. 124 in Proc. of the international conference on operator algebras, ideals, and their applications in theoretical physics, Leipzig, September (1977)]. Some consequences on projective tensor products of Fréchet spaces are indicated.
- Universitat Politècnica de València Spain
- DigiZeitschriften Germany
reduced projective limit of Banach spaces with approximable linking maps, 510.mathematics, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Fréchet Schwartz space with the approximation property, Spaces defined by inductive or projective limits (LB, LF, etc.), Spaces of linear operators; topological tensor products; approximation properties, Tensor products in functional analysis, projective tensor products of Fréchet spaces, Article
reduced projective limit of Banach spaces with approximable linking maps, 510.mathematics, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Fréchet Schwartz space with the approximation property, Spaces defined by inductive or projective limits (LB, LF, etc.), Spaces of linear operators; topological tensor products; approximation properties, Tensor products in functional analysis, projective tensor products of Fréchet spaces, Article
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!