Multiple operator integrals and higher operator derivatives
Multiple operator integrals and higher operator derivatives
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DOI：
10.1016/j.jfa.2005.09.003
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发表时间：
2005-05
影响因子：
1.7
通讯作者：
V. Peller
中科院分区：
文献类型：
--
作者：
V. Peller
本文考虑函数t↦ϕ(A+Tk)的高阶导数的存在性问题，其中ϕ是实直线上的函数，A是自伴算子，K是有界自伴算子。我们改进了Sten‘kin早先的结果。为此，我们给出了多重算子积分的一种新方法。这种方法改进了Sten‘kin早期给出的方法。对于酉算子，我们也考虑了类似的问题。
In this paper we consider the problem of the existence of higher derivatives of the function t↦ϕ(A+tK), where ϕ is a function on the real line, A is a self-adjoint operator, and K is a bounded self-adjoint operator. We improve earlier results by Sten’kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten’kin. We also consider a similar problem for unitary operators.