Publication: Quasinormability and topologies on spaces of polynomials
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Publication Date
1997-09-15
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Elsevier
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Abstract
An example of a Frechet space E is given such that the space of n-homogeneous continuous polynomials on E, endowed with any of the natural topologies usually considered on it, is quasinormable for every n is an element of N. This space has the particularity that all the natural topologies are different on it for n greater than or equal to 2.
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J.M. Ansemil. On the quasinormability of b(U. Extracta Math., 9 (1994), pp. 71–74
J.M. Ansemil, S. Ponte. The compact open and the Nachbin ported topologies on spaces of holomorphic functions. Arch. Math., 51 (1988), pp. 65–70
J.M. Ansemil, J. Taskinen. On a problem of topologies in infinite dimensional holomorphy. Arch. Math., 54 (1990), pp. 61–64
K.D. Bierstedt, J. Bonet. Stefan Heinrich's density condition for Fréchet spaces and the characterization of the distinguished Köthe echelon spaces. Math. Nachr., 135 (1988), pp. 149–180
C. Boyd, A. Peris. A projective description of the Nachbin-ported topology. J. Math. Anal. Appl., 197 (1996), pp. 635–657
F. Blasco. Complementation in spaces of tensor products and polynomials. Studia Math., 123 (1997), pp. 165–173
A. Defant, M. Maestre. Property (BB) and holomorphic functions on Fréchet-Montel spaces. Math. Proc. Cambridge Philos. Soc., 115 (1993), pp. 305–313
S. Dierolf. On spaces of continuous linear mappings between locally convex spaces. Note Mat., 5 (1985), pp. 147–255
S. Dineen. Complex analysis in locally convex spaces. North-Holland Math. Stud., 57North-Holland, Amsterdam (1981)
S. Dineen. Holomorphic functions on Fréchet-Montel spaces. J. Math. Anal. Appl., 163 (1992), pp. 581–587
S. Dineen. Quasinormable spaces of holomorphic functions. Note Mat., 12 (1993), pp. 155–195
S. Dineen. Holomorphic functions and the (BB)-property. Math. Scand., 74 (1994), pp. 215–236
S. Dineen. Complex analysis on infinite dimensional spaces
P. Galindo, D. Garcı́a, M. Maestre. The coincidence of τ0ω. Proc. Roy. Irish Acad. Sect. A, 91 (1991), pp. 137–143
A. Grothendieck. Sur les espaces (F) and (DF). Summa Brasil. Math., 3 (1954), pp. 57–122
A. Grothendieck. Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc., 16 (1955)
H. Jarchow. Locally Convex SpacesTeubner, Stuttgart (1981)
G. Köthe. Topological Vector Spaces, ISpringer-Verlag, New York/Berlin (1969)
E. Nelimarkka. On spaces of holomorphic functions on locally convex spaces defined by an operator ideal. L. Holmström (Ed.), Notes on Funct. Anal., II, Univ. of Helsinki (1980), pp. 25–35
A. Peris, 1992. Productos Tensoriales de Espacios Localmente Convexos Casinormables y otras Clases Relacionadas, Universitat de Valencia, Spain
A. Peris. Topological tensor products of a Fréchet-Schwartz space and a Banach space. Studia Math., 106 (1993), pp. 189–196
R. Ryan. 1980, Applications of Topological Tensor Products to Infinite Dimensional Holomorphy, Trinity College of Dublin, Ireland
J. Taskinen. Examples of non-distinguished Fréchet Spaces. Ann. Acad. Sci. Fenn. Ser. A I Math., 14 (1989), pp. 75–88