Displaying similar documents to “The sets of convergence of power series B 0 -algebras”

A lifting theorem for locally convex subspaces of L 0

R. Faber (1995)

Studia Mathematica

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We prove that for every closed locally convex subspace E of L 0 and for any continuous linear operator T from L 0 to L 0 / E there is a continuous linear operator S from L 0 to L 0 such that T = QS where Q is the quotient map from L 0 to L 0 / E .

On the second order derivatives of convex functions on the Heisenberg group

Cristian E. Gutiérrez, Annamaria Montanari (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ( U )

Sean Dineen (1973)

Annales de l'institut Fourier

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This article is devoted to a study of locally convex topologies on H ( U ) (where U is an open subset of the locally convex topological vector space E and H ( U ) is the set of all complex valued holomorphic functions on E ). We discuss the following topologies on H ( U ) : (a) the compact open topology I 0 , (b) the bornological topology associated with I 0 , (c) the ported topology of Nachbin I ω , (d) the bornological topology associated with I ω  ; and ...