摘要
Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub’s theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.
Holub proved that any bounded linear operator T or ?T defined on Banach space L1(μ) satisfies Daugavet equation 1 + ∥T ∥ = Max {∥I + T ∥, ∥I ?T ∥ }. Holub’s theorem is generalized to the nonlinear case: any nonlinear Lipschitz operatorf defined on Banach space l1 satisfies 1 + L(f) = Max {L(I +f), L(I?f)}, where L(f) is the Lipschitz constant off. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.
基金
DoctorateFoundationofXi’anJiaotongUniversity .
