Remarks about Schlumprecht space
Remarks about Schlumprecht space
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发表时间：
1998
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通讯作者：
D. Kutzarova
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作者：
D. Kutzarova
设S表示Schlumprecht空间。我们证明了1。l∞在S中是不相交的; 2. S包含一个l1扩散模型; 3.对任意自然数序列（nk），S同构于空间（∑∞ k=1 <$lnk ∞）S .设（ei）∞ i=1是线性空间c 00的标准基，即所有n-支撑序列的集合。对于x = ∞ ∑ i=1 aiei ∈ c 0 0，suppx表示集合{i ∈ N：ai 6= 0}. N的子集E称为区间，如果存在a，B使得E = {c ∈ N：a < c < B}.对于N的有限子集E，F，E < F意味着maxE < minF或E是空集。对于x = ∞ ∑ i=1 aiei和N的子集E，Ex表示向量Ex = ∑ i∈ Eaiei。设f：[1，∞）→ [1，∞）是由f（x）= log 2（x+1）定义的函数。Schlumprecht空间S =（S，n·n）是c 0 0关于范数n·n的完备化，它满足下面的隐式方程：（1）n x n = max {n x n ∞，sup E1
Let S denote the Schlumprecht space. We prove that 1. l∞ is finitely disjointly respresentable in S; 2. S contains an l1-spreading model; 3. for any sequence (nk) of natural numbers, S is isomorphic to the space ( ∑∞ k=1⊕ lnk ∞ ) S . Let (ei) ∞ i=1 be the standard basis of the linear space c00, the set of all finitely supported sequences. For x = ∞ ∑ i=1 aiei ∈ c00, suppx denotes the set {i ∈ N : ai 6= 0}. A subset E of N is said to be an interval if there exist a, b such that E = {c ∈ N : a < c < b}. For finite subsets E,F of N, E < F means maxE < minF or E is an empty set. For x = ∞ ∑ i=1 aiei and a subset E of N, Ex denotes the vector Ex = ∑ i∈E aiei. Let f : [1,∞) → [1,∞) be the function defined by f(x) = log2(x+1). The Schlumprecht space S = (S, ‖ · ‖) is the completion of c00 with respect to the norm ‖ · ‖ which satisfies the following implicit equation: (1) ‖x‖ = max { ‖x‖∞, sup E1