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Hermitian operators on Banach algebras of Lipschitz functions


Authors: Fernanda Botelho, James Jamison, A. Jiménez-Vargas and Moisés Villegas-Vallecillos
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
Published electronically: May 30, 2014
MathSciNet review: 3238422
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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.


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Additional Information

Fernanda Botelho
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
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

DOI: https://doi.org/10.1090/S0002-9939-2014-12048-X
Keywords: Spaces of Lipschitz functions, hermitian operator, derivation, bi-circular projection
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.