Displaying similar documents to “Розмернось и мягкие пучки”

Volume ratios in L p -spaces

Yehoram Gordon, Marius Junge (1999)

Studia Mathematica

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There exists an absolute constant c 0 such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that i n f e l l i p s o i d ε ⊂ B E ( v o l ( B E ) / v o l ( ε ) ) 1 / n ≤ c 0 i n f z o n o i d Z ⊂ B F ( v o l ( B F ) / v o l ( Z ) ) 1 / k . The concept of volume ratio with respect to ℓ p -spaces is used to prove the following distance estimate for 2 ≤ q ≤ p < ∞ : s u p F ⊂ ℓ p , d i m F = n i n f G ⊂ L q , d i m G = n d ( F , G ) ∼ c p q n ( q / 2 ) ( 1 / q - 1 / p ) .