On transitive operator algebras in real Banach spaces
On transitive operator algebras in real Banach spaces
复制标题
论实Banach空间中的传递算子代数
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Yuriĭ V. Turovskiĭ
中科院分区：
文献类型：
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作者：
E. Kissin;V. Shulman;Yuriĭ V. Turovskiĭ
.考虑真实的Banach空间中包含非零紧算子的弱闭传递算子代数（Lomonosov代数）.它表明，它们自然分为三类：代数的真实的，复杂的和四元数类。给出了每类代数的性质和特征，并给出了一些有用的例子。证明了在可分的真实的Hilbert空间中存在复型和四元数型两两非相似的Lomonosov代数的连续统。
. 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.