论文标题
在一类归纳限制上构建良好的运算符（b）类型的操作员
Constructing Well-bounded Operators not of type (B) on a Class of Inductive Limits
论文作者
论文摘要
结合良好的运营商是Banach Space $ X $上的线性操作员，该$ X $具有$ ac [a，b] $ functional Ockulus，用于某些间隔$ [a，b] $。如果可以将其作为针对频谱的预测家族不可或缺的组成部分，那么良好的操作员是类型（b），而当$ x $是反射性的情况下，总是这种情况。在非反射空间上有良好的运算符的示例不为（b），并且是否有一个非反射性的Banach空间，每个有良好的操作员都有（b）类型。 Pisier构建的空间回答了否定的Grothendieck的猜想。在本文中，将表明，在包含这些空间的一类Banach空间上，总有一个良好的操作员而不是类型（B）。
Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of projections, and this is always the case when $X$ is reflexive. There are many examples of well-bounded operators on non-reflexive spaces that are not of type (B), and it is open whether there is a non-reflexive Banach space upon which every well-bounded operator is of type (B). The spaces constructed by Pisier, which answered a conjecture of Grothendieck in the negative, have been suggested by Cheng and Doust as a candidate to answer this open problem. In this paper, it will be shown that on a class of Banach spaces containing these spaces, there is always a well-bounded operator not of type (B).
