On decompositions of Banach spaces of continuous functions on Mrówka's spaces

Author:
Piotr Koszmider

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2137-2146

MSC (2000):
Primary 03E50, 46E15, 54G12

DOI:
https://doi.org/10.1090/S0002-9939-05-07799-3

Published electronically:
February 25, 2005

MathSciNet review:
2137881

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Abstract: It is well known that if is infinite compact Hausdorff and scattered (i.e., with no perfect subsets), then the Banach space of continuous functions on has complemented copies of , i.e., . We address the question if this could be the only type of decompositions of into infinite-dimensional summands for infinite, scattered. Making a special set-theoretic assumption such as the continuum hypothesis or Martin's axiom we construct an example of Mrówka's space (i.e., obtained from an almost disjoint family of sets of positive integers) which answers positively the above question.

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Additional Information

**Piotr Koszmider**

Affiliation:
Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, São Paulo, Sp CEP: 05315-970, Brazil

Email:
piotr@ime.usp.br

DOI:
https://doi.org/10.1090/S0002-9939-05-07799-3

Keywords:
Banach spaces of continuous functions,
few operators,
scattered spaces,
almost disjoint families

Received by editor(s):
July 24, 2003

Received by editor(s) in revised form:
April 15, 2004

Published electronically:
February 25, 2005

Additional Notes:
The author acknowledges support from CNPQ, Processo Número 300369/01-8, from FAPESP, Processo Número 02/03677-7 and from Centre de Recerca Matemática at Universidad Autonoma de Barcelona.

Communicated by:
Alan Dow

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.