论文标题
在真实Banach空间中的瞬态操作员代数
On transitive operator algebras in real Banach spaces
论文作者
论文摘要
我们认为含有实际Banach空间中的非零紧凑型操作员（Lomonosov代数）的操作员的弱闭合透射代数。结果表明，它们自然分为三类：真实，复杂和季节类别的代数。介绍了每个类别中代数的特性和特征以及一些有用的示例。结果表明，在可分离的真实希尔伯特空间中，有一个成对的非相似的Lomonosov代数的连续性，具有复杂类型和四元素类型。
We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and quaternion classes. The properties and characterizations of algebras in each class as well as some useful examples are presented. It is shown that in separable real Hilbert spaces there is a continuum of pairwise non-similar Lomonosov algebras of complex type and of quaternion type.
