The range of a projection of small norm in l 1 n

M. Zippin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integers n 〉>0, if Q is a projection of l 1 n onto a k-dimensional subspace E with {norm of matrix}|Q{norm of matrix}|≦1+∈ then there is an integer h〉=k(1-Φ(∈)) and an h-dimensional subspace F of E with d(F,l 1 h ) 〈= 1+Φ (∈) where d(X, Y) denotes the Banach-Mazur distance between the Banach spaces X and Y. Moreover, there is a projection P of l 1 n onto F with {norm of matrix}|P{norm of matrix}| ≦1+Φ(∈).

Original languageEnglish
Pages (from-to)349-358
Number of pages10
JournalIsrael Journal of Mathematics
Volume39
Issue number4
DOIs
StatePublished - Dec 1981

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