An extension of a Bourgain–Lindenstrauss–Milman inequality
نویسندگان
چکیده
Let ‖ · ‖ be a norm on Rn. Averaging ‖(ε1x1, · · · , εnxn)‖ over all the 2n choices of −→ε = (ε1, · · · , εn) ∈ {−1,+1}n, we obtain an expression ‖|x‖| which is an unconditional norm on Rn. Bourgain, Lindenstrauss and Milman [3] showed that, for a certain (large) constant η > 1, one may average over ηn (random) choices of −→ ε and obtain a norm that is isomorphic to ‖| · ‖|. We show that this is the case for any η > 1.
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