Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 35, No 4, (2010), 371p-386p
It was shown in  that the most natural equalities valid for every rank-one operator T in real Banach spaces lead either to the Daugavet equation ||I+T|| = 1 + ||T|| or to the equation ||I − T|| = ||I+T||. We study if the spaces where the latter condition is satisfied for every finite-rank operator inherit the properties of Daugavet spaces.