Metric characterization of first Baire class linear forms and octahedral norms

Gilles Godefroy

Displaying similar documents to “Metric characterization of first Baire class linear forms and octahedral norms”

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

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For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset...

Complemented subalgebras of the Baire-1 functions defined on the interval $[0, 1]$ .

Shatery, H.R. (2005)

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Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

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Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where...

Boundaries of convex sets.

M. Valdivia (1993)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces

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On norm-attaining functionals

Maria D. Acosta, Vicente Montesinos (2006)

Acta Universitatis Carolinae. Mathematica et Physica

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Some Applications of Simons’ Inequality

Godefroy, Gilles (2000)

Serdica Mathematical Journal

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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

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Let K be a compact Hausdorff space, $C_{p} (K)$ the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and $t_{p} (D)$ the topology in C(K) of pointwise convergence on D. It is proved that when $C_{p} (K)$ is Lindelöf the $t_{p} (D)$ -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and $C_{p} (K)$ is Lindelöf, then K is metrizable if, and only if, there is a countable...

Unordered Baire-like spaces without local convexity.

Jerzy Kakol, Walter Roelcke (1992)

Collectanea Mathematica

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The aim of the present paper is to study the class of tvs which we define by ommiting the word increasing in the definition of *-suprabarrelled spaces. We prove that the product of Baire tvs is *-UBL and hence the class of *-UBL spaces is stricty larger than the class of Baire spaces.