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Some remarks on universality properties of $ℓ_∞/c₀$

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Krupski M., Marciszewski W.

Colloquium Mathematicum

2012

tom 128

nr 2

187-195

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 $ℓ_∞/c₀$. 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. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $ℓ_∞/c₀$, but fails to embed isometrically. As far as we know it is the first example of this kind.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Krupski M.

1 Marciszewski W.

1 2012

Wyniki wyszukiwania

Some remarks on universality properties of $ℓ_∞/c₀$