论文标题
没有最大的适当操作员理想
There is no largest proper operator ideal
论文作者
论文摘要
如果其包含的$ id_x $的唯一运算符具有有限的等级，则操作员理想是正确的。我们回答了Pietsch（1979）提出的一个问题，证明没有最大的适当操作员理想。我们的证明是基于Aiena-González（2000）对建筑的扩展，该建筑是通过对$ x_s $的Powers of Powers of Powers of Powers of powers的代数分析的Gowers-Maurey Shift Space $ X_S $（1997）的基础操作员。我们还证明，当一般$ \ mathbb {c} $ - 线性操作员且仅当它们适合这些操作员被视为真实时：例如，这是对严格奇异，严格的，严格的cosing骨或不必要的操作员的理想，回答González-Herrra（2007）的问题。这为我们提供了一个将Pietsch问题的负面答案扩展到真实环境的框架。
An operator ideal is proper if the only operators of the form $Id_X$ it contains have finite rank. We answer a question posed by Pietsch (1979) by proving that there is no largest proper operator ideal. Our proof is based on an extension of the construction by Aiena-González (2000), of an improjective but essential operator on Gowers-Maurey's shift space $X_S$ (1997), through a new analysis of the algebra of operators on powers of $X_S$. We also prove that certain properties hold for general $\mathbb{C}$-linear operators if and only if they hold for these operators seen as real: for example this holds for the ideals of strictly singular, strictly cosingular, or inessential operators, answering a question of González-Herrera (2007). This gives us a frame to extend the negative answer to the question of Pietsch to the real setting.
