Facial Topologies for Subspaces of C(X).
In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015
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.
Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène , au sens de Katznelson, de muni de la topologie engendrée par les semi-normes portées par les compacts de , est bornologique.
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.