Complexifications of real operator spaces
Complexifications of real operator spaces
复制标题
实算子空间的复化
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Z. Ruan
中科院分区：
文献类型：
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作者：
Z. Ruan
研究了真实的算子空间的复化。我们证明了对每个真实的算子空间V，在其复化Vc = V +今iV上存在唯一的复算子空间矩阵范数{n·<$n}，它扩展了V上的原矩阵范数，且满足条件<$x+ iy <$n =<$x− iy <$n，对所有x+ iy ∈Mn（Vc）= Mn（V）+今iMn（V）.作为这一结果的结果，我们刻画了复算子空间，它可以表示为某些真实的算子空间的复化。最后，我们证明了真实的算子空间的某些性质与其复化的相应性质密切相关。
We study the complexifications of real operator spaces. We show that for every real operator space V there exists a unique complex operator space matrix norm {‖ ·‖n} on its complexification Vc = V +̇ iV which extends the original matrix norm on V and satisfies the condition ‖x+ iy‖n = ‖x− iy‖n for all x+ iy ∈Mn(Vc) = Mn(V ) +̇ iMn(V ). As a consequence of this result, we characterize complex operator spaces which can be expressed as the complexification of some real operator space. Finally, we show that some properties of real operator spaces are closely related to the corresponding properties of their complexifications.