Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-14T01:11:48.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Analyticity and quasi-Banach valued functions

Published online by Cambridge University Press:  17 April 2009

Antonio Bernal  and
Joan Cerdà
Antonio Bernal
Affiliation:
Department de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
Joan Cerdà
Affiliation:
Department de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compare the definitions of analyticity of vector-valued functions and their connections with the topological tensor products of non-locally convex spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 369 - 382
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Aleksandrov, A.B., ‘Essays on non locally convex Hardy classes’, in Complex Analysis and Spectral Theory: Lecture Notes in Math 864, Editors Havin, V.P. and Nikolskii, N.K. (Springer-Verlag, Berlin, Heidelberg, New York, 1981).CrossRefGoogle Scholar
[2]Bernal, A. and Cerdà, J., ‘On non locally convex tensor products’, (1989) (preprint).Google Scholar
[3]Coifman, R.R. and Rochberg, R., ‘Representation theorems for holomorfic and harmonic functions in Lp’, Astérisque 77 (1980), 11–66.Google Scholar
[4]Etter, D.O., ‘Vector-valued analytic functions’, Trans. Amer. Math. Soc. 119 (1965), 352–366.CrossRefGoogle Scholar
[5]Gramsch, B., ‘Integration und holomorphe Funktionen in lokalbeschränkten Räumen’, Math. Annal. 162 (1965), 190–210.CrossRefGoogle Scholar
[6]Gramsch, B., ‘Tensorprodukte und integration vektorwertiger funktionen’, Math. Z. 100 (1967), 106–122.CrossRefGoogle Scholar
[7]Gramsch, B. and Vogt, D., ‘Holomorphe funktionen mit Werten in nicht lokalkonvexen Vektorräumen’, J. Reine Angew. Math. 243 (1970), 159–170.Google Scholar
[8]Kalton, N.J., ‘Analytic functions in non-locally convex spaces and applications’, Studia Math. 83 (1986), 275–303.CrossRefGoogle Scholar
[9]Kalton, N.J., ‘Plurisubharmonic functions on quasi-Banach spaces’, Studia Math. 84 (1986), 297–324.CrossRefGoogle Scholar
[10]Kalton, N.J., Peck, N.T. and Roberts, W., ‘An F-space sampler’, London Math. Soc. Lecture Note Ser. 89. (Cambridge Univ. Press 1984).Google Scholar
[11]Peetre, J., ‘Locally analytically pseudo-convex topological vector spaces’, Studia Math. 73 (1982), 252–262.CrossRefGoogle Scholar
[12]Turpin, P., ‘Convexités dans les espaces vectoriels topologiques généraux’, Dissertationes Math. (Rozprawy Mat.) 131 (1974).Google Scholar
[13]Turpin, P., ‘Produits tensoriels d'espaces vectoriels topologiques’, Bull. Soc. Math. France 110 (1982), 3–13.Google Scholar
[14]Turpin, P., ‘Représentation fonctionnelle des espaces vectoriels topologiques’, Studia Math. 73 (1982), 1–10.CrossRefGoogle Scholar
[15]Vogt, D., ‘Integrationstheorie in p-normieten Räumen’, Math. Ann. 173 (1967), 219–232.CrossRefGoogle Scholar
[16]Waelbroeck, L., ‘The tensor product of a locally pseudo-convex and a nuclear space’, Studia Math. 38 (1970), 101–104.CrossRefGoogle Scholar