Journal article
The noncommutative Löwner theorem for matrix monotone functions over operator systems
Linear algebra and its applications, v 541, pp 54-59
15 Mar 2018
Abstract
Given a function f:(a,b)→R, Löwner's theorem states f is monotone when extended to self-adjoint matrices via the functional calculus, if and only if f extends to a self-map of the complex upper half plane. In recent years, several generalizations of Löwner's theorem have been proven in several variables. We use the relaxed Agler, McCarthy, and Young theorem on locally matrix monotone functions in several commuting variables to generalize results in the noncommutative case. Specifically, we show that a real free function defined over an operator system must analytically continue to a noncommutative upper half plane as map into another noncommutative upper half plane.
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Details
- Title
- The noncommutative Löwner theorem for matrix monotone functions over operator systems
- Creators
- J.E. Pascoe
- Publication Details
- Linear algebra and its applications, v 541, pp 54-59
- Publisher
- Elsevier
- Grant note
- DMS 1606260 / National Science Foundation Mathematical Science Postdoctoral Research Fellowship (https://doi.org/10.13039/100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000424724000004
- Scopus ID
- 2-s2.0-85037377832
- Other Identifier
- 991021879630104721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied