算子代数的斜积
On Skew Product of Operator Algebras
{引入了算子代数的一种新运算“斜积”,证明了在这个新定义的斜积运算下算子代数的自反性保持不变.研究发现,斜积运算对应的子空间格是拓扑意义下的格的直积关系.这个新发现的重要意义在于由此可从已知的自反子空间格生成更多更复杂的新自反格,从而得到新的自反代数.在此基础上,本文对KS-代数保持性等其他非自伴代数类的性质也作了相应研究.
A new operation, skew product, of operator algebras is introduced. We show that reflexivity of operator algebras is preserved under the skew product. Thus many new reflexive algebras can be constructed. We also show that the skew product of two KS-algebras is, in general, not a KS-algebra.
von Neumann代数 / Kadison-Singer代数 / 自反代数 {{custom_keyword}} /
von Neumann algebras / Kadison-Singer algebras / reflexive algebras {{custom_keyword}} /
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国家自然科学基金资助项目(11371290)
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