Kernels of trace class operators
Kernels of trace class operators
复制标题
跟踪类运算符的内核
DOI：
10.1090/s0002-9939-1988-0929421-x
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发表时间：
1988
影响因子：
1.2
通讯作者：
C. Brislawn
中科院分区：
文献类型：
--
作者：
C. Brislawn
设XCRn，K是L2（X）上的迹类算子，对应的核为K（x，y）EL 2（XxX）.积分公式TR K，证明了Duflo连续核，推广到任意迹类核。这个公式被证明是等价的一个涉及到的希尔伯特-施密特算子的乘积K的因式分解。该公式及其推导给出了Hilbert-Schmidt核的可溯性的两个新的必要条件，并且证明了这些条件对于正算子也是充分的。证明利用了HardyLittlewood极大函数在L2（Rn）上的有界性。
Let X C Rn and let K be a trace class operator on L2(X) with corresponding kernel K(x, y) E L2(X x X). An integral formula for tr K, proven by Duflo for continuous kernels, is generalized for arbitrary trace class kernels. This formula is shown to be equivalent to one involving the factorization of K into a product of Hilbert-Schmidt operators. The formula and its derivation yield two new necessary conditions for traceability of a Hilbert-Schmidt kernel, and these conditions are also shown to be sufficient for positive operators. The proofs make use of the boundedness of the HardyLittlewood maximal function on L2(Rn).