Characterization of nuclear Fréchet spaces in which every bounded set is polar
Seán Dineen, Reinhold Meise, Dietmar Vogt (1984)
Bulletin de la Société Mathématique de France
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Seán Dineen, Reinhold Meise, Dietmar Vogt (1984)
Bulletin de la Société Mathématique de France
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Ed Dubinsky, Dietmar Vogt (1989)
Studia Mathematica
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Dietmar Vogt (2003)
RACSAM
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The paper gives a complete characterization of the subspaces, quotients and complemented subspaces of a stable power series space of infinite type without the assumption of nuclearity, so extending previous work of M. J. Wagner and the author to the nonnuclear case. Various sufficient conditions for the existence of bases in complemented subspaces of infinite type power series spaces are also extended to the nonnuclear case.
Vincenzo Moscatelli, Marilda Simões (1987)
Studia Mathematica
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Markus Poppenberg, Dietmar Vogt (1995)
Studia Mathematica
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The following result is proved: Let denote a power series space of infinite or of finite type, and equip with its canonical fundamental system of norms, R ∈ 0,∞, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) exists iff α is strongly stable, i.e. , and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable,...
Tosun Terzioglu, Dietmar Vogt (1989)
Revista Matemática de la Universidad Complutense de Madrid
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We define two new normability conditions on Fréchet spaces and announce some related results.
Dietmar Vogt (1987)
Studia Mathematica
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José Bonet, Juan Carlos Díaz, Jari Taskinen (1991)
Collectanea Mathematica
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In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are given.
Jörg Krone, Volker Walldorf (1998)
Studia Mathematica
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The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.
Seán Dineen (1995)
Studia Mathematica
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We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces...
T. Pytlik (1974)
Studia Mathematica
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