Compactifications of ω and the Banach space c₀

2016/01/14 by Piotr Drygier, Drygier, Piotr, Grzegorz Plebanek +1
Mathematics · #03E50 #46B26 #46E50 #54D35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:03E50 #msc:28C15 #msc:46B26 #msc:46E50 #msc:54D35 #secondary 28C15

paper · pdf · doi:10.48550/arxiv.1601.03770

20 pages, version of Jan 23, 2016

arxiv created 2016/01/23 · arxiv updated 2016/01/26

Abstract

We investigate for which compactifications γω of the discrete space of natural numbers ω, the natural copy of the Banach space c₀ is complemented in C(γω). We show, in particular, that the separability of the remainder of γω is neither sufficient nor necessary for c₀ being complemented in C(γω) (for the latter our result is proved under the continuum hypothesis). We analyse, in this context, compactifications of ω related to embeddings of the measure algebra into P(ω)/fin. We also prove that a Banach space C(K) contains a rich family of complemented copies of c₀ whenever the compact space K admits only measures of countable Maharam type.

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• When does C(K,X) contain a complemented copy of c₀(Γ) iff X does?
• Finite compactifications of ω^* ∖ \x\
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