Plus-Minus Property as a Generalization of the Daugavet Property

2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42.

It was shown in [2] 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.