@misc{10481/74424,
year = {2022},
month = {4},
url = {http://hdl.handle.net/10481/74424},
abstract = {We show that all the symmetric projective tensor products of a Banach space X
have the Daugavet property provided X has the Daugavet property and either X is an
L1-predual (i.e., X∗
 is isometric to an L1-space) or X is a vector-valued L1-space. In 
the process of proving it, we get a number of results of independent interest. For 
instance, we characterise “localised” versions of the Daugavet property [i.e., Daugavet points and Δ-points introduced in Abrahamsen et al. (Proc Edinb Math Soc 
63:475–496 2020)] for L1-preduals in terms of the extreme points of the topological dual, a result which allows to characterise a polyhedrality property of real
L1-preduals in terms of the absence of Δ-points and also to provide new examples of 
L1-preduals having the convex diametral local diameter two property. These results 
are also applied to nicely embedded Banach spaces [in the sense of Werner (J Funct 
Anal 143:117–128, 1997)] so, in particular, to function algebras. Next, we show 
that the Daugavet property and the polynomial Daugavet property are equivalent for
L1-preduals and for spaces of Lipschitz functions. Finally, an improvement of recent 
results in Rueda Zoca (J Inst Math Jussieu 20(4):1409–1428, 2021) about the Daugavet property for projective tensor products is also obtained.},
organization = {ACyT Región de Murcia

20797/PI/18},
organization = {Universidad de Granada and Junta de Analucía},
organization = {Fundación Séneca},
organization = {European Commission},
organization = {European Regional Development Fund},
organization = {Junta de Andalucía

FJC2019-039973, FQM-0185, MCIN/AEI/10.13039/501100011033, MTM2017-86182-P},
organization = {University of the East

FQM-185},
publisher = {Birkhauser},
keywords = {Daugavet property},
keywords = {Polynomial Daugavet property},
keywords = {Symmetric tensor  product},
keywords = {Projective tensor product},
keywords = {L1-predual},
title = {Daugavet property in projective symmetric tensor products  of Banach spaces},
doi = {10.1007/s43037-022-00186-6},
author = {Rueda Zoca, Abraham and Martín Suárez, Miguel},
}