Hermitian operators on Banach algebras of Lipschitz functions
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- by Fernanda Botelho, James Jamison, A. Jiménez-Vargas and Moisés Villegas-Vallecillos PDF
- Proc. Amer. Math. Soc. 142 (2014), 3469-3481 Request permission
Abstract:
For compact metric spaces $(X,d)$, we show that the Lipschitz spaces $\mathrm {Lip}(X,d)$ and the little Lipschitz spaces $\mathrm {lip}(X,d^\alpha )$ with $0<\alpha <1,$ equipped with the sum norm, support only trivial hermitian operators, that is, real multiples of the identity operator.References
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Additional Information
- Fernanda Botelho
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- MR Author ID: 252424
- Email: mbotelho@memphis.edu
- James Jamison
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- Email: jjamison@memphis.edu
- A. Jiménez-Vargas
- Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
- Email: ajimenez@ual.es
- Moisés Villegas-Vallecillos
- Affiliation: Campus Universitario de Puerto Real, Facultad de Ciencias, Nuestra Universidad, 11510 Puerto Real, Cádiz, Spain
- Email: moises.villegas@uca.es
- Received by editor(s): February 6, 2012
- Received by editor(s) in revised form: September 5, 2012, September 13, 2012, and October 9, 2012
- Published electronically: May 30, 2014
- Additional Notes: The third and fourth authors were partially supported by Junta de Andalucía grants FQM-3737 and FQM-194 and by MICINN project MTM 2010-17687.
- Communicated by: Thomas Schlumprecht
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3469-3481
- MSC (2010): Primary 46E15, 47B15, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-2014-12048-X
- MathSciNet review: 3238422