Operator Lipschitz estimates in the unitary setting
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- by P. J. Ayre, M. G. Cowling and F. A. Sukochev
- Proc. Amer. Math. Soc. 144 (2016), 1053-1057
- DOI: https://doi.org/10.1090/proc/12833
- Published electronically: August 5, 2015
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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 $V$.References
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Bibliographic 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
- MR Author ID: 52360
- ORCID: 0000-0003-0995-3054
- Email: m.cowling@unsw.edu.au
- F. A. Sukochev
- Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
- MR Author ID: 229620
- Email: f.sukochev@unsw.edu.au
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1053-1057
- MSC (2010): Primary 47A55; Secondary 47B10
- DOI: https://doi.org/10.1090/proc/12833
- MathSciNet review: 3447659