论文标题
完全粗大的地图为$ \ MATHBB R $ -LINEAR
Completely coarse maps are $\mathbb R$-linear
论文作者
论文摘要
如果操作员空间之间的地图完全粗糙，则如果其放大的序列是等效的。我们证明，所有完全粗大的地图都必须是$ \ Mathbb r $ -linear。在此结果的相反方向上，我们引入了操作员空间之间的嵌入性概念，并表明该概念严格比完整的$ \ Mathbb r $ iSomorphic嵌入性（尤其是比完整的$ \ Mathbb C $ -ISomorphic-iSomorphic嵌入性）要弱（特别是弱）。尽管较弱，但对于某些应用，这个概念足够强大。例如，我们表明，如果一个无限的操作员空间$ x $以这种弱的感觉嵌入到皮西尔的操作员空间$ \ mathrm {oh} $中，则$ x $必须完全同构至$ \ m athrm {oh {oh} $。
A map between operator spaces is called completely coarse if the sequence of its amplifications is equi-coarse. We prove that all completely coarse maps must be $\mathbb R$-linear. On the opposite direction of this result, we introduce a notion of embeddability between operator spaces and show that this notion is strictly weaker than complete $\mathbb R$-isomorphic embeddability (in particular, weaker than complete $\mathbb C$-isomorphic embeddability). Although weaker, this notion is strong enough for some applications. For instance, we show that if an infinite dimensional operator space $X$ embeds in this weaker sense into Pisier's operator space $\mathrm{OH}$, then $X$ must be completely isomorphic to $\mathrm{OH}$.
