论文标题
免费的复杂Banach格子
Free complex Banach lattices
论文作者
论文摘要
真正的Banach空间生成的免费Banach晶格的构建扩展到复杂的环境。结果表明，对于每个复杂的Banach空间$ e $，都有一个复杂的Banach晶格$ fbl _ {\ Mathbb c} [e] $，其中包含$ e $的线性等距副本，并满足以下通用属性：对于每个复杂的Banach Lattice $ x _ {\ Mathb c} $ x _ {晶格同构扩展$ \ hat {t}：fbl _ {\ mathbb c} [e] \ rightarrow x _ {\ mathbb c} $ at $ \ | \ | \ hat {t} \ | = \ | = \ | = \ |免费的复杂的Banach晶格$ FBL _ {\ Mathbb C} [E] $显示出与其真实对应物的属性相似的属性。但是，可以给出非晶状体复杂的Banach Spaces $ E $和$ f $的示例，以便$ fbl _ {\ Mathbb c} [e] $和$ fbl _ {\ Mathbb c} [f] $是lattice Isometric。还探索了$ fbl _ {\ mathbb c} [e] $的诱导晶格同态的光谱理论。
The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space $E$ there is a complex Banach lattice $FBL_{\mathbb C}[E]$ containing a linear isometric copy of $E$ and satisfying the following universal property: for every complex Banach lattice $X_{\mathbb C}$, every operator $T:E\rightarrow X_{\mathbb C}$ admits a unique lattice homomorphic extension $\hat{T}:FBL_{\mathbb C}[E]\rightarrow X_{\mathbb C}$ with $\|\hat{T}\|=\|T\|$. The free complex Banach lattice $FBL_{\mathbb C}[E]$ is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces $E$ and $F$ can be given so that $FBL_{\mathbb C}[E]$ and $FBL_{\mathbb C}[F]$ are lattice isometric. The spectral theory of induced lattice homomorphisms on $FBL_{\mathbb C}[E]$ is also explored.
