SOME REMARKS ON UNIVERSALITY PROPERTIES OF l(infinity)/c(0)

作者：Krupski Mikolaj^*; Marciszewski Witold

来源：Colloquium Mathematicum, 2012, 128(2): 187-195.

DOI：10.4064/cm128-2-4

• C(K) spaces
• uniform Eberlein compact
• Kunen cardinal
• universal space

We prove that if c is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into l(infinity)/c(0). We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorcevic. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into l(infinity)/c(0), but fails to embed isometrically. As far as we know it is the first example of this kind.

• 出版日期2012