Log-majorizations and norm inequalities for exponential operators
Log-majorizations and norm inequalities for exponential operators
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DOI：
10.4064/-38-1-119-181
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
F. Hiai
中科院分区：
文献类型：
--
作者：
F. Hiai
对优化理论和对称赋范理想进行了简明而完整的评述，包括Lidskii-Wielandt定理和Gelfand-Naimark定理的证明。在此基础上，我们讨论了Hilbert空间上指数算子的Golden-Thompson型及其补型的对数控制和范数不等式。此外，我们还得到了指数乘积公式和涉及算子平均的乘积公式的范数收敛。
Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii–Wielandt and the Gelfand– Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden–Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.