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Lipschitz slices and the Daugavet equation for Lipschitz operators


Authors: Vladimir Kadets, Miguel Martín, Javier Merí and Dirk Werner
Journal: Proc. Amer. Math. Soc. 143 (2015), 5281-5292
MSC (2010): Primary 46B04; Secondary 46B80, 46B22, 47A12
DOI: https://doi.org/10.1090/proc/12818
Published electronically: July 30, 2015
MathSciNet review: 3411146
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer to the non-linear case some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators.


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Additional Information

Vladimir Kadets
Affiliation: Department of Mechanics and Mathematics, Kharkiv National University, pl. Svobody 4, 61077 Kharkiv, Ukraine
Email: vova1kadets@yahoo.com

Miguel Martín
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: mmartins@ugr.es

Javier Merí
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: jmeri@ugr.es

Dirk Werner
Affiliation: Department of Mathematics, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
Email: werner@math.fu-berlin.de

DOI: https://doi.org/10.1090/proc/12818
Keywords: Numerical radius, numerical index, Daugavet equation, Daugavet property, SCD space, Lipschitz operator
Received by editor(s): September 25, 2014
Published electronically: July 30, 2015
Additional Notes: The work of the first named author was partially done during his visit to the University of Granada in June and July 2013 under the support of Spanish MINECO and FEDER project no. MTM2012-31755. The second and third authors were partially supported by Spanish MICINN and FEDER project no. MTM2012-31755 and by Junta de Andalucía and FEDER grants FQM-185 and P09-FQM-4911.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society

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