Three classes of smooth Banach submanifolds in B(E,F)

查看全文 作　　者：Ji-pu Ma Tseng Yaun Rong Functional Analysis Research Center,Harbin Normal University,Harbin 150025,China

出　　处：《Science China Mathematics》索引2007年第50卷第9期,共7页

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No.10671049) 摘　　要：Let E,F be two Banach spaces,and B(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be the bounded linear,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively.In this paper,using the continuity characteristics of generalized inverses of operators under small perturba- tions,we prove the following result:Let∑be any one of the following sets:{T∈Φ(E,F):IndexT= const,and dim N(T)=const.},{T∈SΦ(E,F):either dim N(T)=const.<∞or codim R(T)=const.<∞} and {T∈R(E,F):RankT=coast.<∞}.Then∑is a smooth submanifold of B(E,F) with the tangent space T_A∑={B∈B(E,F):BN(A)(?)R(A)} for any A∈∑.The result is available for the further application to Thom’s famous results on the transversility and the study of the infinite dimensional geometry. 关键词：semi-Fredholm OPERATORS SMOOTH SUBMANIFOLD transversility generalized inverse

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Three classes of smooth Banach submanifolds in B(E,F)

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