Displaying similar documents to “On nuclear maps between spaces of ultradiferentiables jets of Roumieu type.”

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...

Summable families in nuclear groups

Wojciech Banaszczyk (1993)

Studia Mathematica

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Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.

On multilinear mappings of nuclear type.

Mário C. Matos (1993)

Revista Matemática de la Universidad Complutense de Madrid

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The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.