Quasi-isometric liftings for operators similar to contractions

IF 1 3区 数学 Q1 MATHEMATICS
Laurian Suciu, Andra-Maria Stoica
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引用次数: 0

Abstract

A class of quasi-isometric liftings for the operators T similar to contractions in Hilbert spaces H is studied. These liftings are isometric operators on their ranges, and are naturally induced by T and an invertible intertwiner of T with a contraction. In the case when T is a quasicontraction, meaning that T is contractive on its range, we obtain a quasi-isometric lifting on a space KH, which is isometric on KH. Some liftings with closed ranges, or even similar to quasinormal partial isometries are mentioned. Additionally, we study the isomorphic minimal quasi-isometric liftings for T, as well as the uniqueness property of such liftings. Our results show similarities with those from the isometric dilation theory for contractions, although our context is more general than that of the latter.
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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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