准对称空间的压缩可补子空间
Contractively complemented subspaces of pre-symmetric spaces
摘要：
1965年，Ron Douglas证明了如果$X$是$L^1$ -空间的闭子空间，并且$X$与另一个$L^1$ -空间等距，则$X$是包含$L^1$ -空间上的压缩投影的值域。在1977年阿拉兹弗里德曼表明，如果一个子空间$X$的$C_1$是等距的另一个$C_1$ -空间（可能有限维），那么有一个压缩投影的$C_1$到$X$。1993年Kirchberg证明了如果一个冯诺依曼代数$M$的预对偶的子空间$X$与另一个冯诺依曼代数的预对偶等距，则存在一个$M$的预对偶到$X$上的压缩投影。我们显着扩大了这些结果的范围，通过表明，如果一个$JBW^*$ -三重$A$的前对偶的子空间$X$是等距的另一个$JBW^*$ -三重$B$的前对偶，那么有一个压缩投影的$A$的前对偶范围$X$，只要$B$没有一个直接的和是等距的形式$L^\infty(Ω,H)$的空间，其中，$H$是维度至少为2的希尔伯特空间。如果对$B$没有此限制，则结果为假。
英文摘要：
In 1965, Ron Douglas proved that if $X$ is a closed subspace of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$ is the range of a contractive projection on the containing $L^1$-space. In 1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric to another $C_1$-space (possibly finite dimensional), then there is a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved that if a subspace $X$ of the predual of a von Neumann algebra $M$ is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of $M$ onto $X$. We widen significantly the scope of these results by showing that if a subspace $X$ of the predual of a $JBW^*$-triple $A$ is isometric to the predual of another $JBW^*$-triple $B$, then there is a contractive projection on the predual of $A$ with range $X$, as long as $B$ does not have a direct summand which is isometric to a space of the form $L^\infty(Ω,H)$, where $H$ is a Hilbert space of dimension at least two. The result is false without this restriction on $B$.
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