论文标题
在不可分割的C* - 代理中几乎不可估计的套件
Uncountable almost irredundant sets in nonseparable C*-algebras
论文作者
论文摘要
在本文中，我们考虑了几乎不冗余集的概念：c*-algebra $ \ algebra $ \ nathcal {a} $的子集$ \ nathcal {x} $几乎被称为irredixtion，并且仅当每个$ a \ in \ in \ mathcal in \ nathcal {x} $中，元素$ a $ a $ a $ a $ a $ a $ cul of nard n n nord o n n n n nord i cluse i cluse i cluse i cluse i cluse i cluse i y = i \ r { λ_i\ prod_ {j = 1}^{n_i} a_ {i，j}：\ textrm {where} a_ {i，j} \ in \ mathcal {x} \ setMinus \ setMinus \ setMinus \ \ \ \ \ \ \ \}特别是一个离散集，因此，$ \ MATHCAL {a} $的密度是几乎不差的集合大小的上限。我们证明，在适当的强迫公理（PFA）下，每个c* - 代数都有一个无法数的几乎不繁殖设置，其理想序列不可超数。特别是，假设PFA，每个不可分割的散射C* - 代数都承认一个几乎不可数的不可分割的集合。
In this article, we consider the notion of almost irredundant sets: A subset $\mathcal{X}$ of a C*-algebra $\mathcal{A}$ is called almost irredundant if and only if for every $a\in \mathcal{X}$, the element $a$ does not belong to the norm-closure of $$\{\sum_{i=1}^n λ_i \prod_{j=1}^{n_i}a_{i,j}: \textrm{ where } a_{i,j} \in \mathcal{X}\setminus\{a\} \textrm{ and} \sum |λ_i|\leq 1\}.$$ Since every almost irrredundant set is in particular a discrete set, it follows that the density of $\mathcal{A}$ is an upper bound for the size of almost irredundant sets. We prove that under the Proper Forcing Axiom (PFA), there is an uncountable almost irredundant set in every C*-algebra with an uncountable increasing sequence of ideals. In particular, assuming PFA, every nonseparable scattered C*-algebra admits an uncountable almost irredundant set.
