矩阵代数中一类新的Kadison-Singer格

New Kadison-Singer Lattices in Matrix Algebras

摘要: 本文在矩阵代数M₂(C)和M₃(C)中由一个极大套和由一个分离向量决定的秩1投影生成的Kadison-Singer格及Kadison-Singer代数的基础上，将该类投影分别嵌入到矩阵代数M₄(C)与M₆(C)中，构造出了生成M₄(C)与M₆(C)的Kadison-Singer格并计算出了相应的Kadison-Singer代数。

Abstract: For given Kadison-Singer lattices in  matrix algebras  M₂(C) and M₃(C)  which is generated by a maximal nest and rank 1 operator determined by a separating vector, the paper constructs new Kadison-Singer lattices in M₄(C) and  M₆(C)which generate the full matrix algebras M₄(C)  and  M₆(C)respectively.