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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Corson compacta and embeddings of $ C(K)$ spaces


Authors: Witold Marciszewski and Grzegorz Plebanek
Journal: Proc. Amer. Math. Soc. 138 (2010), 4281-4289
MSC (2010): Primary 46B26, 46E15; Secondary 46E27
Published electronically: May 17, 2010
MathSciNet review: 2680054
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Abstract: We investigate properties of those compact spaces $ K$ for which the Banach space $ C(K)$ can be isomorphically embedded into a space $ C(L)$, where $ L$ is Corson compact. We show that in such a case $ K$ must be Corson compact provided $ K$ has some additional measure-theoretic property. The result is applicable to Rosenthal compacta and several other classes of compact spaces $ K$.


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Additional Information

Witold Marciszewski
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02–097 Warszawa, Poland
Email: wmarcisz@mimuw.edu.pl

Grzegorz Plebanek
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: grzes@math.uni.wroc.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10403-3
PII: S 0002-9939(2010)10403-3
Received by editor(s): September 11, 2009
Received by editor(s) in revised form: January 24, 2010
Published electronically: May 17, 2010
Additional Notes: Research of the first author was partially supported by MNiSW Grant No. N N201 382034.
The second author was partially supported by grant 2191/W/IM/09 from the University of Wrocław.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society