| 刘建忠,江波.半序线性空间上线性泛函的两个Gr\"{u}ss型不等式$^{}$[J].数学年刊A辑,2014,35(3):257~266 |
| 半序线性空间上线性泛函的两个Gr\"{u}ss型不等式$^{}$ |
| Two Gr¨uss Type Inequalities for Linear Functionals in the Partially Ordered LinearSpace |
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| DOI： |
| 中文关键词: 半序线性空间, Gr\"{u}ss 型不等式, Karamata型不等式, Hilbert空间, 张量积 |
| 英文关键词:Partially ordered linear space, Gr\"{u}ss type inequality,
Karamata type inequality, Hilbert space, Tensor product |
| 基金项目:国家自然科学基金(No.11102076) |
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| 中文摘要: |
| 证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式,
得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式.
最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式. |
| 英文摘要: |
| By proving two Gr\"{u}ss type inequalities for linear functional in partially ordered linear space,
and then a generalization of the Karamata type integral inequality, a new Gr\"{u}ss type integral
inequality is established and two inequalities on Fourier coefficients are given.
As an application,
some Gr\"{u}ss type inequalities of matrices and linear operators are also studied. |
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