A note on Tsirelson type ideals

• Autorzy: Boban Veličković
• Języki publikacji: EN

Abstrakty

EN

Using Tsirelson's well-known example of a Banach space which does not contain a copy of $c_0$ or $l_p$, for p ≥ 1, we construct a simple Borel ideal $I_T$ such that the Borel cardinalities of the quotient spaces $P(ℕ)/I_T$ and $P(ℕ)/I_0$ are incomparable, where $I_0$ is the summable ideal of all sets A ⊆ ℕ such that $∑ _{n ∈ A}1/(n+1) < ∞$. This disproves a "trichotomy'' conjecture for Borel ideals proposed by Kechris and Mazur.

Kategorie tematyczne

• 46Bxx: Normed linear spaces and Banach spaces; Banach lattices
• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 3
• Strony: 259-268

Daty

wydano

1999

otrzymano

1998-04-10

Twórcy

autor

Boban Veličković

• UFR de Mathématiques, Université Paris 7, 2 Place Jussieu, 75251 Paris, France

Bibliografia

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