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
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 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
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 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.
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.
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.
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.
