A Dvoretsky Theorem for Polynomials

نویسنده

  • Seán Dineen
چکیده

We lift upper and lower estimates from linear functionals to n-homogeneous polynomials and using this result show that l ∞ is finitely represented in the space of n-homogeneous poly-nomials, n ≥ 2, for any infinite dimensional Banach space. Refinements are also given. The classical Dvoretsky spherical sections theorem [5,13] states that l 2 is finitely represented in any infinite dimensional Banach space. Using this, the Riesz Representation theorem (for finite dimensional l p spaces) and the Hahn-Banach theorem we show that l ∞ is finitely represented in P(n E), for any infinite dimensional Banach space and any n ≥ 2. This shows that P(n E) does not have any non-trivial superproperties and explains why spaces such as Tsirelson's space play such a positive role in the recent theory of polyno-for properties of Banach spaces and to [4] for properties of polynomials.

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تاریخ انتشار 1994