On decompositions of Banach spaces of continuous functions on Mrówka's spaces
Author:
Piotr Koszmider
Journal:
Proc. Amer. Math. Soc. 133 (2005), 21372146
MSC (2000):
Primary 03E50, 46E15, 54G12
Published electronically:
February 25, 2005
MathSciNet review:
2137881
Fulltext PDF Free Access
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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 infinitedimensional summands for infinite, scattered. Making a special settheoretic 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: 05315970, Brazil
Email:
piotr@ime.usp.br
DOI:
http://dx.doi.org/10.1090/S0002993905077993
PII:
S 00029939(05)077993
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 300369/018, from FAPESP, Processo Número 02/036777 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.
