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Algunos nuevos resultados sobre el teorema de la gráfica cerrada.

Manuel Valdivia (1979)

Revista Matemática Hispanoamericana

Para varios espacios localmente separados, damos aplicaciones lineales no continuas con gráficas cerradas. Uno de los resultados obtenidos contiene el teorema de Mahowald como corolario [7]. Si ε es una clase de espacios localmente convexos separados, estable para límites inductivos y conteniendo los espacios de dimensiones finitas, sea εr la clase de todos los espacios localmente convexos separados tales que si E ∈ ε, F ∈ εr y f es una aplicación lineal de E en F con gráfica cerrada, entonces f...

Almost demi Dunford--Pettis operators on Banach lattices

Hedi Benkhaled (2023)

Commentationes Mathematicae Universitatis Carolinae

We introduce new concept of almost demi Dunford–Pettis operators. Let E be a Banach lattice. An operator T from E into E is said to be almost demi Dunford–Pettis if, for every sequence { x n } in E + such that x n → 0 in σ ( E , E ' ) and ∥ x n - T x n ∥ → 0 as n → ∞ , we have ∥ x n ∥ → 0 as n → ∞ . In addition, we study some properties of this class of operators and its relationships with others known operators.

AM-Compactness of some classes of operators

Belmesnaoui Aqzzouz, Jawad H'michane (2012)

Commentationes Mathematicae Universitatis Carolinae

We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.

An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

M. Poppenberg (1999)

Studia Mathematica

A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces C ∞ ( K ) , S ( ℝ N ) , B ( ℝ R N ) , D L 1 ( ℝ N ) , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay, Edgar Lee Stout (2000)

Annales de l'institut Fourier

This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

An elementary proof of a theorem on sublattices of finite codimension

Marek Wójtowicz (1998)

Commentationes Mathematicae Universitatis Carolinae

This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property.

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