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Kadec Norms on Spaces of Continuous Functions

Burke, Maxim R.;  Wiesaw, Kubis;  Stevo, Todorcevic — 2006

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35. We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class...

Invariant Borel liftings for category algebras of Baire groups

Maxim R. Burke — 2007

Fundamenta Mathematicae

R. A. Johnson showed that there is no translation-invariant Borel lifting for the measure algebra of ℝ/ℤ equipped with Haar measure, a result which was generalized by M. Talagrand to non-discrete locally compact abelian groups and by J. Kupka and K. Prikry to arbitrary non-discrete locally compact groups. In this paper we study analogs of these results for category algebras (the Borel σ-algebra modulo the ideal of first category sets) of topological groups. Our main results are for the class of...

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