Schlumprecht和Schreier空间上的小算子理想
Small operator ideals on the Schlumprecht and Schreier spaces
摘要：
给出了在巴拿赫空间$X$上构造算子的一种方法，该算子在$X$上的有界线性算子代数$\mathscr{B}(X)$中生成不同的算子理想.证明了Schlumprecht空间上确实存在$2^\mathfrak{c}$不同的小闭算子理想，并且在任何有穷级的Schreier空间上都存在小闭算子理想的基数链$\mathfrak{c}$.
英文摘要：
We present a method of building operators on a Banach space $X$ that generate distinct operator ideals in the algebra $\mathscr{B}(X)$ of bounded linear operators on $X$. We show that there are exactly $2^\mathfrak{c}$ distinct small closed operator ideals on the Schlumprecht space and there is a chain of cardinality $\mathfrak{c}$ of small closed operator ideals on any Schreier space of finite order.
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