On the Weyl functional calculus
On the Weyl functional calculus
复制标题
关于 Weyl 泛函计算
DOI：
10.1016/0022-1236(70)90050-9
复制
发表时间：
1969
影响因子：
1.7
通讯作者：
Robert F. Anderson
中科院分区：
文献类型：
--
作者：
Robert F. Anderson
进一步研究了“Weyl泛函演算”中讨论的自伴算子元组(A)在Rn上的算子值分布T(A)。结果是：1.(1)分布T(A)的支集在Rn中是连通的，除非某个非平凡的正交投影与当时元组(A)中的所有算子交换。(2)在有限维Hilbert空间的特殊情况下，T(A)不能表示为一个测度，除非T(A)中的所有算子都是交换的。第一个结果是通过研究算子(A)是解的算子微分方程的传播得到的。第二个结果是通过对算子元组的数值范围的几何研究而得到的。这些结果被用来比较自伴算子对的Weyl演算和有界算子的密切相关的Riesz演算。
The operator valued distributionT(A) onRnassociated with ann-tuple of self-adjoint operators (A) which was discussed in “The Weyl Functional Calculus” is further studied. The results are:1.(1) The support of the distributionT(A) is connected inRnunless some nontrivial orthogonal projection commutes with all the operators in then-tuple (A).2.(2) In the special case of finite dimensional Hilbert space,T(A) cannot be represented as a measure unless all the operators in then-tuple (A) commute.The first result is obtained by studying the propagation of an operator differential equation of whichT(A) is a solution.The second result is obtained by geometric study of the numerical range of ann-tuple of operators.The results are used to contrast the Weyl calculus for a pair of self-adjoint operators with the closely related Riesz calculus for a bounded operator.