This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ide...This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ideal M and a decomposition into direct sum of ideals about the greatest special sympathetic ideal.Besides,each perfect Jordan algebra J also contains a solvable ideal P(J)which is greatest among the solvable ideals K of J such that K∩M={0}and a decomposition into direct sum of subalgebras J=m+P(J),where m is a sympathetic subalgebra of J,which is similar to the Levi decomposition of Lie algebras.Moreover,J is sympathetic if and only if P(J)={0}.What is more,a class of ideals of Jordan algebras such that the quotients are sympathetic Jordan algebras are studied and some vital properties about this kind of ideal are highlighted.展开更多
For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with ...For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with the algebra B(H)of all bounded linear operators on H,and obtain S_(C)-analogues of some classical results concerning B(H).The authors determine the Jordan ideals of S_(C) and their dual spaces.Jordan automorphisms of S_(C) are classified.The authors determine the spectra of Jordan multiplication operators on S_(C) and their different parts.It is proved that those Jordan invertible ones constitute a dense,path connected subset of S_(C).展开更多
We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan ...We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.展开更多
In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have be...In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.展开更多
In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinit...In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.展开更多
Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to...Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.展开更多
The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order struct...The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order structures of the corresponding spaces. The results are obtained applying or extending previous classical results and methods of Ayupov, Carath6odory, Cohen, Eberlein, Kakutani and Yosida. Moreover, this results can be applied to continious or positive operators appearing in diffusion theory, quantum mechanics and quantum 13robabilitv theory.展开更多
In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.
基金Supported by NNSF of China(Nos.12271085,12071405)NSF of Jilin Province(No.YDZJ202201ZYTS589)the Fundamental Research Funds for the Central Universities and Heilongjiang Provincial Universities Basic Scientific Research Operation Fund Project of Heilongjiang University(No.2022-KYYWF-1114).
文摘This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ideal M and a decomposition into direct sum of ideals about the greatest special sympathetic ideal.Besides,each perfect Jordan algebra J also contains a solvable ideal P(J)which is greatest among the solvable ideals K of J such that K∩M={0}and a decomposition into direct sum of subalgebras J=m+P(J),where m is a sympathetic subalgebra of J,which is similar to the Levi decomposition of Lie algebras.Moreover,J is sympathetic if and only if P(J)={0}.What is more,a class of ideals of Jordan algebras such that the quotients are sympathetic Jordan algebras are studied and some vital properties about this kind of ideal are highlighted.
基金supported by the National Natural Science Foundation of China(Nos.12401149,12171195)the National Key Research and Development Program of China(No.2020YFA0714101).
文摘For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with the algebra B(H)of all bounded linear operators on H,and obtain S_(C)-analogues of some classical results concerning B(H).The authors determine the Jordan ideals of S_(C) and their dual spaces.Jordan automorphisms of S_(C) are classified.The authors determine the spectra of Jordan multiplication operators on S_(C) and their different parts.It is proved that those Jordan invertible ones constitute a dense,path connected subset of S_(C).
基金supported by FAPESP(16/16445-0,18/15712-0),RFBR(18-31-00001)the President's Program Support of Young Russian Scientists(grant MK-2262.2019.1).
文摘We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.
基金supported by the Natural Science Basic Research Program of Shaanxi (Program No. 2023-JCYB-048)the National Natural Science Foundation of China (Program No. 11601406)。
文摘In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.
文摘In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.
基金Supported by the National Natural Science Foundation of China(Grant No.11501401)
文摘Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.
文摘The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order structures of the corresponding spaces. The results are obtained applying or extending previous classical results and methods of Ayupov, Carath6odory, Cohen, Eberlein, Kakutani and Yosida. Moreover, this results can be applied to continious or positive operators appearing in diffusion theory, quantum mechanics and quantum 13robabilitv theory.
基金Fundamental Research Funds (N110423007) for the Central Universities
文摘In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.
