Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=P_(A)BP_(A^(*)),where PA and P_(A^(*))denote projections onto the closu...Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=P_(A)BP_(A^(*)),where PA and P_(A^(*))denote projections onto the closures of R(A)and R(A^(*)),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions.展开更多
Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the...Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the sufficient and necessary condition for f to be such a map.展开更多
We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective ...We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11771261)。
文摘Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=P_(A)BP_(A^(*)),where PA and P_(A^(*))denote projections onto the closures of R(A)and R(A^(*)),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions.
文摘Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the sufficient and necessary condition for f to be such a map.
基金supported in part by a grant from the Ministry of Science of Slovenia
文摘We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.
