Locally convex inductive limits of normed algebras
Alberto Arosio (1974)
Rendiconti del Seminario Matematico della Università di Padova
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Alberto Arosio (1974)
Rendiconti del Seminario Matematico della Università di Padova
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Bosch, Carlos, Kučera, Jan, McKennon, Kelly (1986)
International Journal of Mathematics and Mathematical Sciences
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Seán Dineen (1975)
Bulletin de la Société Mathématique de France
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Gilsdorf, Thomas E. (1989)
International Journal of Mathematics and Mathematical Sciences
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Kari Astala (1982)
Studia Mathematica
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Leonhard Frerick (1993)
Collectanea Mathematica
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Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.
Ansemil, J.M., Ponte, S. (1985-1986)
Portugaliae mathematica
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Susanne Dierolf (1980)
Collectanea Mathematica
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J. M. Isidro (1979)
Revista Matemática Hispanoamericana
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Seán Dineen, Luiza A. Moraes (1992)
Revista Matemática de la Universidad Complutense de Madrid
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In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.