论文标题
Kalton-Peck空间是真正的Kalton-Peck空间的复杂化
The Kalton-Peck space is the complexification of the real Kalton-Peck space
论文作者
论文摘要
Kalton-peck $ Z_2 $空间是从$ 1/2 $的复杂插值从$ \ ell_p $ space获得的派生空间。如果我们用$ z_2^{real} $表示，那么从$（1/2，1/2）$的$ \ ell_p $ space获得的派生空间，我们表明$ z_2 $是$ z_2^{real} $的络合力。我们还表明，$ z_2^{real} $共享$ z_2 $的最重要属性：它与其双重相同，它是奇异的，它不包含$ \ ell_2 $的补充副本。
The Kalton-Peck $Z_2$ space is the derived space obtained from the scale of $\ell_p$ spaces by complex interpolation at $1/2$. If we denote by by $Z_2^{real}$ the derived space obtained from the scale of $\ell_p$ spaces by real interpolation at $(1/2, 1/2)$, we show that $Z_2$ is the complexification of $Z_2^{real}$. We also show that $Z_2^{real}$ shares the most important properties of $Z_2$: it is isomorphic to its dual, it is singular and contains no complemented copies of $\ell_2$.
