%0 Journal Article
%T Nonlinear version of Holub''s theorem and its application<br>
%A Jigen Peng
%A Zongben Xu
%A <br>
%J 科学通报(英文版)
%D 1998
%I 
%X 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.
%K nonlinear Lipschitz operator
%K Holub theorem
%K Daugavet equation
%K invertibility of operator<br>
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=01BA20E8BA813E1908F3698710BBFEFEE816345F465FEBA5&cid=96E6E851B5104576C2DD9FC1FBCB69EF&jid=DD6615BC9D2CFCE0B6F945E8D5314523&aid=DB409AFF61369C50573D070E85941DF4&yid=8CAA3A429E3EA654&vid=BE33CC7147FEFCA4&iid=0B39A22176CE99FB&sid=CFAC5CB624A41AFD&eid=CFAC5CB624A41AFD&journal_id=1001-6538&journal_name=科学通报(英文版)&referenced_num=0&reference_num=5