Each Non-Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse.
Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen.
Ekeland's variational principle in Fréchet spaces and the density of extremal points
By modifying the method of Phelps, we obtain a new version of Ekeland's variational principle in the framework of Fréchet spaces, which admits a very general form of perturbations. Moreover we give a density result concerning extremal points of lower semicontinuous functions on Fréchet spaces. Even in the framework of Banach spaces, our result is a proper improvement of the related known result. From this, we derive a new version of Caristi's fixed point theorem and a density result for Caristi...
El espacio de la convergencia en medida y su dual.
Embeddings of Fréchet spaces in uniform Fréchet algebras
Enlargements of operators between locally convex spaces.
In this note we study three operators which are canonically associated with a given linear and continuous operator between locally convex spaces. These operators are defined using the spaces of bounded sequences and null sequences. We investigate the relation between them and the original operator concerning properties, like being surjective or a homomorphism.
Equivalent nuclear systems
Errata to the article "On holomorphy in Banach spaces and absolute convergence of Fourier series" (Port. Math., 45(4) (1988), 429-450)
Espaces localement convexes séparés différentiables
Espacios de Fréchet de generación debilmente compacta.
Every separable Fréchet space contains a non stable dense subspace
Existence of bases and the dual splitting relation for Fréchet spaces
Existence of best approximations
Extension and splitting theorems for Fréchet spaces of type 2.
We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension of vector-valued holomorphic and harmonic functions
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.