向量值空间中的几何酉元

黄旭剑, 谭冬妮

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 1001-1008.

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数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 1001-1008. DOI: 10.12386/A2015sxxb0099
论文

向量值空间中的几何酉元

    黄旭剑, 谭冬妮
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Geometric Unitaries in Vector-Valued Function Spaces

    Xu Jian HUANG, Dong Ni TAN
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摘要

研究向量值空间中的几何酉元.通过数值指标理论刻画向量值空间C(Ω, X), L∞(μ, X) 和 L(l1(Γ), X)中几何酉元的特征, 其中X是Banach空间, Ω 是紧Hausdorff空间,μ是σ有限测度以及Γ 是非空指标集.同时,描述了Banach空间的内射张量积和投射张量积中几何酉元的特征.

Abstract

We study the geometric unitaries in vector-valued function spaces. By using numerical index theory, we characterize the geometric unitaries in the spaces C(Ω, X) on a compact Hausdorff space Ω, L∞(μ, X) for every σ-finite measure μ and L(l1(Γ),X)for every nonempty index set Γ. We also describe the geometric unitaries in the injective and projective tensor product of Banach spaces.

关键词

几何酉元 / 数值指标 / 数值域空间

Key words

geometric unitary / numerical index / numerical range space

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黄旭剑, 谭冬妮. 向量值空间中的几何酉元. 数学学报, 2015, 58(6): 1001-1008 https://doi.org/10.12386/A2015sxxb0099
Xu Jian HUANG, Dong Ni TAN. Geometric Unitaries in Vector-Valued Function Spaces. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 1001-1008 https://doi.org/10.12386/A2015sxxb0099

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基金

国家自然科学基金(11201337,11201338,11371201,11301384);天津市教委资助项目(20111001)

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