A NULLSTELLENSATZ FOR AMOEBAS

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A CHARACTERIZATION OF SUBSPACES AND QUOTIENTS OF REFLEXIVE BANACH SPACES WITH UNCONDITIONAL BASES W. B. JOHNSON and BENTUO ZHENG Abstract We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property (UTP) has the UTP. This is used to prove that a separable reflexive Banach space with the UTP embeds into a reflexive Banach space with an unconditional basis. This solves several longstanding open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finitedimensional decomposition (UFDD) embeds into a reflexive Banach space with an unconditional basis. 1. Introduction It has long been known that Banach spaces with unconditional bases as well as their subspaces are much better behaved than general Banach spaces and that many of the reflexive spaces (including L p (0, 1), 1
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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
Page 45 and 46: 452 DAVID GINZBURG Proof The proof
Page 47 and 48: 454 DAVID GINZBURG correspond to th
Page 49 and 50: 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: 502 DAVID GINZBURG [GP] S. GELBART
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DISTORTION OF HAUSDORFF MEASURES AN
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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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584 MARCHÉ and NARIMANNEJAD Defini
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586 MARCHÉ and NARIMANNEJAD [A2] [
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