Abstract
We show that there exists k ∈ N and 0 < ε{lunate} ∈ R such that for every field F of characteristic zero and for every n ∈ N, there exist explicitly given linear transformations T1, ..., Tk : Fn → Fn satisfying the following: For every subspace W of Fn of dimension less or equal frac(n, 2), dim (W + ∑i = 1k Ti W) ≥ (1 + ε{lunate}) dim W. This answers a question of Avi Wigderson [A. Wigderson, A lecture at IPAM, UCLA, February 2004]. The case of fields of positive characteristic (and in particular finite fields) is left open.
Original language | English |
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Pages (from-to) | 730-738 |
Number of pages | 9 |
Journal | Journal of Algebra |
Volume | 319 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jan 2008 |
Keywords
- Expander
- Property τ
- Property T