Daugavet centers and direct sums of Banach spaces

摘要

A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies {double pipe}G + T{double pipe} = {double pipe}G{double pipe} + {double pipe}T{double pipe}. We study the case when either X or Y is a sum X_(1?F)X_2 of two Banach spaces X_1 and X_2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X_1 and X_2 there exists a Daugavet center acting from X_(1?F)X_2, and the class of those F such that for some pair of spaces X_1 and X_2 there is a Daugavet center acting into X_(1?F)X_2. We also present several examples of such Daugavet centers.