Contractivity of Möbius functions of operators

IF 1 3区 数学 Q1 MATHEMATICS
Thomas Ransford , Dashdondog Tsedenbayar
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引用次数: 0

Abstract

Let T be an injective bounded linear operator on a complex Hilbert space. We characterize the complex numbers λ,μ for which (I+λT)(I+μT)1 is a contraction, the characterization being expressed in terms of the numerical range of the possibly unbounded operator T1.

When T=V, the Volterra operator on L2[0,1], this leads to a result of Khadkhuu, Zemánek and the second author, characterizing those λ,μ for which (I+λV)(I+μV)1 is a contraction. Taking T=Vn, we further deduce that (I+λVn)(I+μVn)1 is never a contraction if n2 and λμ.

算子莫比乌斯函数的收缩性
设 T 是复希尔伯特空间上的注入有界线性算子。当 T=V (L2[0,1] 上的 Volterra 算子)时,这将引出 Khadkhuu、Zemánek 和第二作者的一个结果,即描述那些 (I+λV)(I+μV)-1 是收缩的 λ,μ 的特征。以 T=Vn 为例,我们进一步推导出,如果 n≥2 且 λ≠μ 时,(I+λVn)(I+μVn)-1 绝不是收缩。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
333
审稿时长
13.8 months
期刊介绍: Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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