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Operator Lipschitz estimates in the unitary setting


Authors: P. J. Ayre, M. G. Cowling and F. A. Sukochev
Journal: Proc. Amer. Math. Soc. 144 (2016), 1053-1057
MSC (2010): Primary 47A55; Secondary 47B10
DOI: https://doi.org/10.1090/proc/12833
Published electronically: August 5, 2015
MathSciNet review: 3447659
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Abstract: We develop a Lipschitz estimate for unitary operators. More specifically, we show that for each $ p\in (1,\infty )$ there exists a constant $ d_p$ such that $ \left \Vert f(U) - f(V)\right \Vert _p \leq d_p \left \Vert U - V\right \Vert _p$ for all Lipschitz functions $ f: \mathbb{T} \to \mathbb{C}$ and unitary operators $ U$ and $ V$.


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Additional Information

P. J. Ayre
Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
Email: peter.ayre@unsw.edu.au

M. G. Cowling
Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
Email: m.cowling@unsw.edu.au

F. A. Sukochev
Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
Email: f.sukochev@unsw.edu.au

DOI: https://doi.org/10.1090/proc/12833
Keywords: Unitary operators, Lipschitz estimates
Received by editor(s): February 9, 2014
Received by editor(s) in revised form: March 28, 2014, and February 4, 2015
Published electronically: August 5, 2015
Communicated by: Marius Junge
Article copyright: © Copyright 2015 American Mathematical Society

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