A NULLSTELLENSATZ FOR AMOEBAS

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510 JOHNSON and ZHENG Let (x A ) be a normalized weakly null tree in X. Thenwelet(E n ) and (F n ) be blockings of (G i ) and (v i ), respectively, which satisfy the conclusions of Lemmas 2.5 and 2.6. Using the “killing the overlap” technique (see [13, Proposition 2.6]), we can find a further blocking ( E˜ n = ⊕ l(n+1) i=l(n)+1 E i) so that for every y ∈ SY , there exist (y i ) ⊂ Y and integers (t i ) with l(i − 1)
A CHARACTERIZATION OF SUBSPACES AND QUOTIENTS 511 This gives an estimate of the second term. For the third term, we have ∥ ∥a i x Ai − ( k 2i−1−1 ∑ P˜ j )x∥ < ∥ ( k 2i−1−1 ∑ P˜ ∥ j )(a i x Ai − x) ∥ + ∥a i x Ai − ( k 2i−1−1 ∑ ∥ P˜ ∥∥ j )x Ai j=k 2i−2 j=k 2i−2 < 2 (k 2i−2 δ k2i−2 + ∑ ) δ j + 2δ i j≥k 2i−1 j=k 2i−2 < 2(δ k2i−2 −1 + δ k2i−1 −1) + 2δ i < 4δ i . (2.4) For the first term, let Q j be the canonical projection from X onto F j ,andletJ 1 = [t k2i−3 +1,t k2i−1 +1],J 2 = [l k2i−2 + 1,l k2i−1 ],andJ 1 ′ = (t k 2i−3 +1,t k2i−1 +1). Thenwehave ( ∥ ∑ ) ( ∑ ) ∥Q P j y − Q j Qy∥ j∈J 1 j∈J 2 ( ∥ ∑ ) ( ∑ ) ( ∑ ) ( ∑ ) ≤ ∥Q P j y − Q j Qy∥ + ∥ Q j Qy − Q j Qy∥ j∈J 1 j∈J 1 j∈J 1 j∈J 2 ( ∥ ∑ ) ( ∑ ) = ∥Q P j y − Q j Qy∥ + ∥ ∑ ( ∑ )∥ ∥∥ Q j ai x Ai j∈J 1 j∈J 1 j∈J 1 −J 2 ( ∥ ∑ ) ( ∑ ) < ∥Q P j y − Q j Qy∥ + 4δ i j∈J 1 j∈J 1 ( ≤ ∑ ) ( ∑ )∥ ∥( ∥∥ ∥∥ ∑ ) ( ∑ )∥ ∥∥ ∥ Q j Q P j y + Q j Q P j y + 4δi j/∈J 1 j∈J 1 j∈J 1 j/∈J 1 ( < ∥ ∑ ( ∑ )∥ ∥( ∥∥ ∥∥ ∑ ( ∑ )∥ ∥∥ Q P j y + Q j )Q + 6δi j/∈J 1 Q j ) j∈J ′ 1 j∈J ′ 1 j/∈J 1 P j y < 2λδ i + 2λδ i + 6δ i = (4λ + 6)δ i . (2.5) From inequalities (2.2)–(2.5), we conclude that ‖Qz i − a i x Ai ‖ < (4λ + 12)δ i . Let (ɛ i ) ⊂{−1, 1} N .LetI ⊂ N be the set of indices i ∈ N for which ‖y i ‖
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A NULLSTELLENSATZ FOR AMOEBAS 443 C
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448 DAVID GINZBURG The method we us
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450 DAVID GINZBURG Let ν denote a
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452 DAVID GINZBURG Proof The proof
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454 DAVID GINZBURG correspond to th
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456 DAVID GINZBURG Next, consider t
Page 51 and 52: 458 DAVID GINZBURG To state the fol
Page 53 and 54: 460 DAVID GINZBURG check that up to
Page 55 and 56: 462 DAVID GINZBURG where L τ (¯s)
Page 57 and 58: 464 DAVID GINZBURG To define the li
Page 59 and 60: 466 DAVID GINZBURG cuspidality of t
Page 61 and 62: 468 DAVID GINZBURG immediately foll
Page 63 and 64: 470 DAVID GINZBURG expansion. Here
Page 65 and 66: 472 DAVID GINZBURG Notice that S l
Page 67 and 68: 474 DAVID GINZBURG values of m ′
Page 69 and 70: 476 DAVID GINZBURG For 1 ≤ i ≤
Page 71 and 72: 478 DAVID GINZBURG 2m rows, we have
Page 73 and 74: 480 DAVID GINZBURG left to right. C
Page 75 and 76: 482 DAVID GINZBURG unipotent orbit
Page 77 and 78: 484 DAVID GINZBURG for every choice
Page 79 and 80: 486 DAVID GINZBURG is equal to L(σ
Page 81 and 82: 488 DAVID GINZBURG Here f π (h) is
Page 83 and 84: 490 DAVID GINZBURG character ψ Um
Page 85 and 86: 492 DAVID GINZBURG Proof The proof
Page 87 and 88: 494 DAVID GINZBURG in the above ref
Page 89 and 90: 496 DAVID GINZBURG THEOREM 7 The ir
Page 91 and 92: 498 DAVID GINZBURG In the above, th
Page 93 and 94: 500 DAVID GINZBURG is GL 2m+1 × SO
Page 95 and 96: 502 DAVID GINZBURG [GP] S. GELBART
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574 MARCHÉ and NARIMANNEJAD them w
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576 MARCHÉ and NARIMANNEJAD 1.1. P
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578 MARCHÉ and NARIMANNEJAD 2.1. T
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580 MARCHÉ and NARIMANNEJAD Figure
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