Matches in SemOpenAlex for { <https://semopenalex.org/work/W199678876> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W199678876 abstract "Let E and X be real Banach and locally convex spaces, respectively. Let Ccn(E,X) denote the space of n times continuously Hadamard differentiable functions f:E→X, endowed with the locally convex topology generated by the seminorms of the form f∈Ccn(E,X)→sup{α[Dpf(x)(y)]:x,y∈K}, where p∈N, p≤n, K⊂E is compact, and α is a continuous seminorm on X. The authors show that Ccn(E,X) is complete if X is complete, and investigate the relationship between approximation in Ccn(E,X) and the approximation property of E. For example, if X is complete, then Ccn(E,X) is topologically isomorphic to the e-product of Ccn(E,R) and X. Using this result, the authors show that the following properties are equivalent: (a) E has the approximation property, (b) Ccn(E,R) has the approximation property for all (equivalently, for some) n≥1, and (c) for all X, Ccn(E,R)⊗X is dense in Ccn(E,X) for all (equivalently, for some) n≥1. Similar questions have been considered for the space Cn(E,X) of n times continuously Frechet differentiable functions, endowed with the same locally convex topology. For example, the equivalence of (a) and (b) was proved by the first author (Differentiable functions with the approximation property'', to appear) and the reviewer [Infinite dimensional holomorphy and applications (Proc. Internat. Sympos., Campinas, 1975), pp. 1–17, North-Holland, Amsterdam, 1977; see also Seminaire Pierre Lelong (Analyse), Annee 1974/75, pp. 213–222, Lecture Notes in Math., Vol. 524, Springer, Berlin, 1976. It is apparently unknown whether Cn(E,R) is complete with this topology. Results relating the approximation property of E to approximation of Frechet differentiable functions defined on open subsets of E and to generalized differentiable versions of the Stone-Weierstrass theorem have been obtained by J. B. Prolla and C. S. Guerreiro [Ark. Mat. 14 (1976), no. 2, 251–258]." @default.
- W199678876 created "2016-06-24" @default.
- W199678876 creator A5020001075 @default.
- W199678876 creator A5078132837 @default.
- W199678876 date "1976-01-01" @default.
- W199678876 modified "2023-09-28" @default.
- W199678876 title "The approximation property in spaces of differentiable functions. (Spanish: La propiedad de aproximación en espacios de funciones diferenciables)." @default.
- W199678876 hasPublicationYear "1976" @default.
- W199678876 type Work @default.
- W199678876 sameAs 199678876 @default.
- W199678876 citedByCount "0" @default.
- W199678876 crossrefType "journal-article" @default.
- W199678876 hasAuthorship W199678876A5020001075 @default.
- W199678876 hasAuthorship W199678876A5078132837 @default.
- W199678876 hasConcept C112680207 @default.
- W199678876 hasConcept C114614502 @default.
- W199678876 hasConcept C118615104 @default.
- W199678876 hasConcept C132954091 @default.
- W199678876 hasConcept C145446738 @default.
- W199678876 hasConcept C156103551 @default.
- W199678876 hasConcept C202444582 @default.
- W199678876 hasConcept C202615002 @default.
- W199678876 hasConcept C2524010 @default.
- W199678876 hasConcept C33923547 @default.
- W199678876 hasConceptScore W199678876C112680207 @default.
- W199678876 hasConceptScore W199678876C114614502 @default.
- W199678876 hasConceptScore W199678876C118615104 @default.
- W199678876 hasConceptScore W199678876C132954091 @default.
- W199678876 hasConceptScore W199678876C145446738 @default.
- W199678876 hasConceptScore W199678876C156103551 @default.
- W199678876 hasConceptScore W199678876C202444582 @default.
- W199678876 hasConceptScore W199678876C202615002 @default.
- W199678876 hasConceptScore W199678876C2524010 @default.
- W199678876 hasConceptScore W199678876C33923547 @default.
- W199678876 hasLocation W1996788761 @default.
- W199678876 hasOpenAccess W199678876 @default.
- W199678876 hasPrimaryLocation W1996788761 @default.
- W199678876 hasRelatedWork W1523043375 @default.
- W199678876 hasRelatedWork W1535281561 @default.
- W199678876 hasRelatedWork W1590316100 @default.
- W199678876 hasRelatedWork W1777744657 @default.
- W199678876 hasRelatedWork W1988583478 @default.
- W199678876 hasRelatedWork W1998644029 @default.
- W199678876 hasRelatedWork W2002445978 @default.
- W199678876 hasRelatedWork W2004530829 @default.
- W199678876 hasRelatedWork W2010037853 @default.
- W199678876 hasRelatedWork W2012103676 @default.
- W199678876 hasRelatedWork W2064130630 @default.
- W199678876 hasRelatedWork W2079577078 @default.
- W199678876 hasRelatedWork W2131836769 @default.
- W199678876 hasRelatedWork W2155126958 @default.
- W199678876 hasRelatedWork W2167380351 @default.
- W199678876 hasRelatedWork W2266978220 @default.
- W199678876 hasRelatedWork W2280349945 @default.
- W199678876 hasRelatedWork W2317070978 @default.
- W199678876 hasRelatedWork W262940389 @default.
- W199678876 hasRelatedWork W3151898791 @default.
- W199678876 isParatext "false" @default.
- W199678876 isRetracted "false" @default.
- W199678876 magId "199678876" @default.
- W199678876 workType "article" @default.