The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matr...The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matrix over an arbitrary ring.Moreover,the weighted Drazin inverse of a rectangular matrices product PAQ can be characterized and computed.This generalizes results obtained for the Drazin inverse of such product of square matrices.The results also apply to morphisms in(additive)categories.展开更多
Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I....Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.展开更多
Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n...Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n∈N is an additive^(*)-higher derivation.In particu-lar,we apply the above result to prime^(*)-algebras and von Neumann algebras with no central summands of typeⅠ1.展开更多
文摘The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matrix over an arbitrary ring.Moreover,the weighted Drazin inverse of a rectangular matrices product PAQ can be characterized and computed.This generalizes results obtained for the Drazin inverse of such product of square matrices.The results also apply to morphisms in(additive)categories.
文摘Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.
基金Supported by the National Natural Science Foundation of China(12271323)。
文摘Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n∈N is an additive^(*)-higher derivation.In particu-lar,we apply the above result to prime^(*)-algebras and von Neumann algebras with no central summands of typeⅠ1.
