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Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

Hironao Koshimizu (2011)

Open Mathematics

We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.

Fonctionnelles analytiques sur certains espaces de Banach

Gérard Cœuré (1971)

Annales de l'institut Fourier

Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène E , au sens de Katznelson, de L 1 ( π ) muni de la topologie engendrée par les semi-normes portées par les compacts de E , est bornologique.

Funciones unimodulares y acotación uniforme.

J. Fernández, S. Hui, Harold S. Shapiro (1989)

Publicacions Matemàtiques

In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.

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