Embeddings of ℓp into Non-commutative Spaces
2003 ◽
Vol 74
(3)
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pp. 331-350
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Keyword(s):
AbstractLet 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].
1991 ◽
Vol 110
(1)
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pp. 169-182
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1981 ◽
Vol 57
(6)
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pp. 303-306
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2001 ◽
Vol 131
(2)
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pp. 363-384
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2003 ◽
Vol 55
(9)
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pp. 1445-1456
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2020 ◽
pp. 89-93
2008 ◽
Vol 337
(2)
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pp. 1226-1237
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Keyword(s):
2008 ◽
Vol 19
(04)
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pp. 481-501
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2018 ◽
Vol 38
(2)
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pp. 429-440
Keyword(s):