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The Daugavet equation for Lipschitz operators
Multi angle
Authors : Werner, Dirk (Author of the conference)
CIRM (Publisher )
46B04 - Isometric theory of Banach spaces
46B22 - Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
47A12 - Numerical range, numerical radius
46B80 - Nonlinear classification of Banach spaces; nonlinear quotients
CIRM (Publisher )
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Abstract :
We study the Daugavet equation
$\parallel Id+T\parallel$ $=1$ $+$ $\parallel T\parallel$
for Lipschitz operators on a Banach space. For this we introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators to the non-linear case.
Keywords : numerical radius; numerical index; Daugavet equation; Daugavet property; SCD space; Lipschitz operator
MSC Codes : $\parallel Id+T\parallel$ $=1$ $+$ $\parallel T\parallel$
for Lipschitz operators on a Banach space. For this we introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators to the non-linear case.
Keywords : numerical radius; numerical index; Daugavet equation; Daugavet property; SCD space; Lipschitz operator
46B04 - Isometric theory of Banach spaces
46B22 - Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
47A12 - Numerical range, numerical radius
46B80 - Nonlinear classification of Banach spaces; nonlinear quotients
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/01/15 Conference Date : 15/01/15 Subseries : Research talks arXiv category : Functional Analysis Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:47:27 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-01-15_Werner.mp4 
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Information on the Event
Event Title : Banach spaces and their applications in analysis / Espaces de Banach et applications à l'analyseEvent Organizers : Albiac, Fernando ; Casazza, Peter G. ; Godefroy, Gilles ; Lancien, Gilles Dates : 12/01/15 - 16/01/15 Event Year : 2015
Citation Data
DOI : 10.24350/CIRM.V.18666703Cite this video as: Werner, Dirk (2015). The Daugavet equation for Lipschitz operators. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18666703 URI : http://dx.doi.org/10.24350/CIRM.V.18666703 |
Bibliography
- Kadets, V., Martin, M., Meri, J., & Werner, D. (2014). Lipschitz slices and the Daugavet equation for Lipschitz operators.
