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
By characterizing the bijections preserving orthogonality of idempotents in both directions on the infinite dimensional complete indefinite inner product spaces,we obtain the concrete form of surjective maps completel...By characterizing the bijections preserving orthogonality of idempotents in both directions on the infinite dimensional complete indefinite inner product spaces,we obtain the concrete form of surjective maps completely preserving indefinite Jordan 1-†-zero product between†-standard operator algebras.Our results show that such maps are nonzero constant multiple of isomorphisms or conjugate isomorphisms.展开更多
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By characterizing the bijections preserving orthogonality of idempotents in both directions on the infinite dimensional complete indefinite inner product spaces,we obtain the concrete form of surjective maps completely preserving indefinite Jordan 1-†-zero product between†-standard operator algebras.Our results show that such maps are nonzero constant multiple of isomorphisms or conjugate isomorphisms.
