Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Baire classes of Banach spaces and strongly affine functions

Author: Jirí Spurny
Journal: Trans. Amer. Math. Soc. 362 (2010), 1659-1680
MSC (2000): Primary 46A55; Secondary 26A21
Published electronically: October 20, 2009
MathSciNet review: 2563744
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a metrizable simplex $ X$ and a Baire-two function $ f$ on $ X$ satisfying the barycentric formula such that $ f$ is not of affine class two; i.e., there is no bounded sequence of affine Baire-one functions on $ X$ converging to $ f$. This provides an example of a Banach $ \mathcal{L}_\infty$-space $ E$ such that $ E_{2}^{**}\neq E_{\mathcal{B}_2}^{**}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46A55, 26A21

Retrieve articles in all journals with MSC (2000): 46A55, 26A21

Additional Information

Jirí Spurny
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Keywords: Simplex, strongly affine functions, barycentric formula, Baire functions, $L^1$--preduals, intrinsic Baire classes
Received by editor(s): May 24, 2007
Received by editor(s) in revised form: June 4, 2008
Published electronically: October 20, 2009
Additional Notes: This research was supported in part by the grants GA ČR 201/06/0018, GA ČR 201/07/0388, and in part by the Research Project MSM 0021620839 from the Czech Ministry of Education.
Article copyright: © Copyright 2009 American Mathematical Society

American Mathematical Society