The Daugavet property of a Banach space 
is the identity
 |
for every rank-one bounded operator 
, where 
is the identity operator.
It imposes a norm-geometric condition on all such operators.
Daugavet Property
See also
Asymptotic Midpoint Uniform Convexity, Asymptotic Uniform Convexity, Banach Space, Bounded OperatorExplore with Wolfram|Alpha
References
Kadets, V. M.; Shvidkoy, R. V.; Sirotkin, G. G.; and Werner, D. "Banach Spaces with the Daugavet Property." Trans. Amer. Math. Soc. 352, 855-873, 2000. https://doi.org/10.1090/S0002-9947-99-02377-6.Cite this as:
Weisstein, Eric W. "Daugavet Property." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DaugavetProperty.html