Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Reinhold Meise, Dietmar Vogt (1986)
Studia Mathematica
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Displaying similar documents to “Characterization of nuclear Fréchet spaces in which every bounded set is polar”
Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Holomorphic functions on fully nuclear spaces
Philip J. Boland, Seán Dineen (1978)
Bulletin de la Société Mathématique de France
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(LB)-structure of spaces of germs of holomorphic functions.
Nguyen Dinh Lan (2000)
Publicacions Matemàtiques
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We study the structure of spaces of germs of holomorphic functions on compact sets in Fréchet spaces for (LB) as well as for (Ω,Ω).
Nuclear spaces on a locally compact group
T. Pytlik (1974)
Studia Mathematica
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On nuclear maps between spaces of ultradiferentiables jets of Roumieu type.
Jean Schmets, Manuel Valdivia (2003)
RACSAM
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Si K es un compacto no vacío en R, damos una condición suficiente para que la inyección canónica de ε(K) en ε(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε(F) en ε(R) donde F es un subconjunto cerrado propio de R y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.
Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis
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.
Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces
Manfred Scheve (1991)
Studia Mathematica
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Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from...
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
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...
Fréchet spaces with quotients failing the bounded approximation property
Ed Dubinsky, Dietmar Vogt (1985)
Studia Mathematica
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On weak and Schauder decompositions
M. de Wilde (1972)
Studia Mathematica
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Structure theory of power series spaces of infinite type.
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.