Anderson铺路图的几个新等价式
Some new equivalences of Anderson's paving conjectures
摘要：
安德森的铺路问题被认为是等价于凯迪逊-辛格问题。我们证明了一些新的等价的安德森的代数，需要铺路较小的矩阵集。证明了如果严格上三角算子是可铺的，则每一个0对角算子都是可铺的。这一结果来自一个新的铺路条件，积极的运营商。另外，证明了如果上三角Toeplitz算子是可铺的，则所有Toeplitz算子都是可铺的.
英文摘要：
Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operatorss are pavable, then every 0 diagonal operator is pavable. This result follows from a new paving condition for positive operators. In addition, we prove that if the upper triangular Toeplitz operators are paveable, then all Toeplitz operators are paveable.
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