非交换加权Lorentz空间的对偶空间

韩亚洲, 吐尔德别克

数学学报 ›› 2016, Vol. 59 ›› Issue (1) : 117-132.

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数学学报 ›› 2016, Vol. 59 ›› Issue (1) : 117-132. DOI: 10.12386/A2016sxxb0012
论文

非交换加权Lorentz空间的对偶空间

    韩亚洲, 吐尔德别克
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The Dual of Noncommutative Weighted Lorentz Spaces

    Ya Zhou HAN, Turdebek N. BEKJAN
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摘要

M 是一个半有限von Neumann代数. 对于< p < ∞, 0 < q ≤ ∞, 定义了非交换加权 Lorentz 空间Λωp,q (M) 及其 associate 空间Λωp,q(M)', 给出了空间Λωp,q(M) 和 Λωp,q(M)' 的一些基本性质.应用这些性质,还给出了非交换加权 Lorentz 空间Λωp,q(M), 0< p< ∞ 的对偶空间.

Abstract

Let M be a semifinite von Neumann algebra. For 0 < p < ∞, 0 < q ≤ ∞, we define the noncommutative weighted Lorentz spaces Λωp,q (M) and its associate spaces Λωp,q (M)'. Subsequently, we give some properties of the spaces Λωp,q(M) and Λωp,q(M)'. As an application, the dual spaces of Λωp,q(M) is presented for 0 < p < ∞.

关键词

von Neumann 代数 / 非交换加权 Lorentz 空间 / 对偶空间

Key words

von Neumann algebras / noncommutative weighted Lorentz spaces / dual spaces

引用本文

导出引用
韩亚洲, 吐尔德别克. 非交换加权Lorentz空间的对偶空间. 数学学报, 2016, 59(1): 117-132 https://doi.org/10.12386/A2016sxxb0012
Ya Zhou HAN, Turdebek N. BEKJAN. The Dual of Noncommutative Weighted Lorentz Spaces. Acta Mathematica Sinica, Chinese Series, 2016, 59(1): 117-132 https://doi.org/10.12386/A2016sxxb0012

参考文献

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基金

国家自然科学基金资助项目(11371304, 11401507)

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