Embeddings of ℓp into Non-commutative Spaces
Embeddings of ℓp into Non-commutative Spaces
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DOI：
10.1017/s1446788700003359
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发表时间：
2003-06
影响因子：
0.7
通讯作者：
N. Randrianantoanina
中科院分区：
文献类型：
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作者：
N. Randrianantoanina
设ℳ是半有限von Neumann代数，具有忠实的正规迹τ。证明了ń-Pelczy Rademacher型可测算子对称空间子空间的Kadec-Pelczy Rademacher型二分性原理，研究了非对易ℳ，τ空间Lp，Q，(Lp)的子空间结构，推广了Carthers和Dilworth的一些结果.特别地，我们证明了在指数的自然条件下，ℓp不能嵌入到Lp，q(ℳ，τ)中。作为应用，我们证明了对于0<；p<；∞和p≠2，ℓp不能强嵌入到Lp(ℳ，τ)中。这提供了0<；p<；1的Kalton结果和1≦p<；2的Rosenthal结果在Lp[0，1]上的一个非对易推广。
Abstract Let ℳ be a semi-finite von Neumann algebra equipped with a faithful normal trace τ. We prove a Kadec-Pelczyński type dichotomy principle for subspaces of symmetric space of measurable operators of Rademacher type 2. We study subspace structures of non-commutative Lorentz spaces Lp, q, (ℳ, τ), extending some results of Carothers and Dilworth to the non-commutative settings. In particular, we show that, under natural conditions on indices, ℓp cannot be embedded into Lp, q (ℳ, τ). As applications, we prove that for 0 < p < ∞ with p ≠ 2, ℓp cannot be strongly embedded into Lp(ℳ, τ). This provides a non-commutative extension of a result of Kalton for 0 < p < 1 and a result of Rosenthal for 1 ≦ p < 2 on Lp [0, 1].