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Marek W´ojtowicz ) IDHJ FHB  EBJEC B FHA?JE FHFAHJEAI E 4EAI IF=?AI

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Marek W´ ojtowicz

A short proof on lifting of projection properties in Riesz spaces

Comment.Math.Univ.Carolinae 40,2 (1999) 277-278.

Abstract: Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Aucan be lifted toLis given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties ofC(X)-spaces. Similar results are obtained for the Riesz spacesBn(T),n= 1,2, ..., of all functions of the nth Baire class on a metric spaceT.

Keywords: Dedekind completeness, spaces of continuous functions, spaces of Baire functions

AMS Subject Classification: 46A40, 26A99, 46B30

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