Geodesic
Generalized Daugavet equations, affine operators and unique best approximation
Paweł Wójcik1
1 Institute of Mathematics Pedagogical University of Cracow Podchorążych 2 30-084 Kraków, Poland
Studia Mathematica, Tome 238 (2017) no. 3, pp. 235-247

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We introduce and investigate the notion of generalized Daugavet equation $\| A_1+\cdots +A_n\| =\| A_1\| +\cdots +\| A_n\| $ for affine operators $A_1,\ldots ,A_n$ on a reflexive Banach space into another Banach space. This extends the well-known Daugavet equation $\| T+I\| =\| T\| +1$, where $I$ denotes the identity operator. A new characterization of the Daugavet equation in terms of extreme points is given. We also present a result concerning uniqueness of best approximation.
DOI : 10.4064/sm8635-12-2016
Keywords: introduce investigate notion generalized daugavet equation cdots cdots affine operators ldots reflexive banach space another banach space extends well known daugavet equation where denotes identity operator characterization daugavet equation terms extreme points given present result concerning uniqueness best approximation

Paweł Wójcik 1

1 Institute of Mathematics Pedagogical University of Cracow Podchorążych 2 30-084 Kraków, Poland 
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Paweł Wójcik. Generalized Daugavet equations, affine operators and unique best approximation. Studia Mathematica, Tome 238 (2017) no. 3, pp. 235-247. doi: 10.4064/sm8635-12-2016

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