论文标题
操作员的正交谎言代数：理想和推导
The orthogonal Lie algebra of operators: ideals and derivations
论文作者
论文摘要
我们在本文中研究了无限二二维正交谎言代数$ \ Mathcal {o} _c $，由所有有界的线性算子组成，可分开，无限尺寸，复杂的希尔伯特space $ \ mathcal $ \ Mathcal {h} $ \ MATHCAL {H} $。通过采用复杂的对称运算符和偏斜对称运算符理论的结果，我们确定了$ \ Mathcal {O} _C $及其双空间的谎言理想。我们研究$ \ Mathcal {O} _C $的推导，并确定它们的光谱。这些结果完成了P. de la Harpe的一些结果，并在$ \ MATHCAL {H} $上的所有有界线性运算符的$ \ Mathcal {O} _C $与代数$ \ Mathcal {B（H）} $之间提供了有趣的对比。
We study in this paper the infinite-dimensional orthogonal Lie algebra $\mathcal{O}_C$ which consists of all bounded linear operators $T$ on a separable, infinite-dimensional, complex Hilbert space $\mathcal{H}$ satisfying $CTC=-T^*$, where $C$ is a conjugation on $\mathcal{H}$. By employing results from the theory of complex symmetric operators and skew-symmetric operators, we determine the Lie ideals of $\mathcal{O}_C$ and their dual spaces. We study derivations of $\mathcal{O}_C$ and determine their spectra. These results complete some results of P. de la Harpe and provide interesting contrasts between $\mathcal{O}_C$ and the algebra $\mathcal{B(H)}$ of all bounded linear operators on $\mathcal{H}$.
