On decompositions of Banach spaces of continuous functions on Mrowka's spaces
By Piotr Koszmider. 2005
49 citations recorded by the source corpus.
It is well known that if K is infinite compact Hausdorff and scattered (i.e., with no perfect subsets), then the Banach space C(K) of continuous functions on K has complemented copies of c 0 , i.e., C(K) ∼ c 0 ○+ X ∼ c 0 ○+ c 0 ○+ X ∼ c 0 ○+ C(K). We address the question if this could be the only type of decompositions of C(K)? c 0 into infinite-dimensional summands for K infinite, scattered. Making a special set-theoretic assumption such as the continuum hypothesis or Martin's axiom we construct an example of Mrowka's space (i.e., obtained from an almost disjoint family of sets of positive integers) which answers positively the above question.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6dd6efce0f4adaec8f7fd08002c8b24efb8d8353
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In Applied Mathematics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Almost Disjoint Families and Topology (2014, background): “These spaces have proved to be rather flexible and versatile sources of examples in many areas of topology ranging from the study of Fréchet and sequential spaces [43, 45, 47, 145], hyperspaces [89] and continuous selections [85, 90] to Cp-theory [51, 84] and functional analysis [59, 60, 101, 113, 1”
- Banach spaces of continuous functions with few operators (2004, background): “Using some ideas of this paper, it is possible (at least at the price of an additional set-theoretic assumption) to obtain a dispersed compact K such that all operators on C(K) are of the form cI + S where c is a real and S has the range included in c0 (see [ Ko2 ]).”