论文标题
在最佳投影常数下Banach空间的等距嵌入
Isometric embeddings of Banach spaces under optimal projection constants
论文作者
论文摘要
令$ x $为带有可分离双重的Banach空间。可以证明，（0,1）$，$ x $嵌入的每一个$ \ varepsilon \ in（$ x $）嵌入到banach space $ w $中，带有缩水基础$（w_n）$，是$（1+ \ varepsilon）$ - 单调。此外，如果$ x $进一步具有FDD $（E_N）$，其强大的双重频率投影常数不大于$ \ Mathcal {d} $，则$（W_N）$具有强大的双极性投影常数，但不超过$ \ Mathcal {D}（1 +\ varepsilon）$。此外，如果$（e_n）$是$ \ MATHCAL {C} $ - 无条件，则$（w_n）$为$ \ MATHCAL {C}（1 + \ VAREPSILON）$ - 无条件。该证明使用重新分配和跳过阻塞分解技术。作为一个应用程序，我们证明每个Banach空间都具有$ \ Mathcal {d} $ - 无条件的基础，具有$ \ Mathcal {d} <\ sqrt {6} -1 $，具有较弱的固定点属性。
Let $X$ be a Banach space with separable dual. It is proved that for every $\varepsilon\in (0,1)$, $X$ embeds isometrically into a Banach space $W$ with a shrinking basis $(w_n)$ which is $(1+ \varepsilon)$-monotone. Moreover, if $X$ has further an FDD $(E_n)$ whose strong bimonotonicity projection constant is not larger than $\mathcal{D}$, then $(w_n)$ has strong bimonotonicity projection constant not exceeding $\mathcal{D}(1 +\varepsilon)$. Further, if $(E_n)$ is $\mathcal{C}$-unconditional then $(w_n)$ is $\mathcal{C}(1 + \varepsilon)$-unconditional. The proof uses renorming and skipped blocking decomposition techniques. As an application, we prove that every Banach space having a shrinking $\mathcal{D}$-unconditional basis with $\mathcal{D}<\sqrt{6}-1$, has the weak fixed point property.
