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

• Autorzy: Mikołaj Krupski , Witold Marciszewski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 03E75: Applications of set theory
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 2
• Strony: 187-195

Daty

wydano

2012

Twórcy

autor

Mikołaj Krupski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Witold Marciszewski

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm128-2-4