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At the Origins of Functional Analysis: G. Peano and M. Gramegna on Ordinary Differential Equations

Erika Luciano (2006)

Revue d'histoire des mathématiques

In the context of the theory of infinite matrices and linear operators, two articles by Peano and by Gramegna on systems of linear differential equations have interesting implications for the reconstruction of research on functional analysis between 1887 and 1910. With the aim of evaluating their historical value, linked to logic and vector calculus, this paper provides a detailed analysis of their treatment, demonstrating the modernity of the analytic tools used. In this paper we also reveal the...

Atomic decomposition of a weighted inductive limit.

Jari Taskinen (2003)

RACSAM

Estudiamos algunas cuestiones estructurales acerca del espacio localmente convexo HV∞, que está formado por funciones analíticas en el disco unidad abierto. Construimos una descomposición atómica de este espacio, usando un retículo de puntos del disco unidad que es más denso que el usual. También demostramos que HV∞ no es nuclear.

Atomic decomposition on Hardy-Sobolev spaces

Yong-Kum Cho, Joonil Kim (2006)

Studia Mathematica

As a natural extension of L p Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.

Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples

María Burgos, Jorge J. Garcés, Antonio M. Peralta (2011)

Studia Mathematica

We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there exists a (not...

Automatic continuity of biseparating maps

Jesús Araujo, Krzysztof Jarosz (2003)

Studia Mathematica

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

Automatic continuity of operators commuting with translations

J. Alaminos, J. Extremera, A. R. Villena (2006)

Studia Mathematica

Let τ X and τ Y be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that Φ ∘ τ X ( t ) = τ Y ( t ) ∘ Φ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

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