We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We repr...We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We represent weighted geometric mean preserving bijective maps on the positive cones of prime C^(*)-algebras in terms of Jordan *-isomorphisms of the algebras.We also characterize order isomorphisms and orthoisomorphisms of the projection lattice of the von Neumann algebra of all bounded linear operators on a Hilbert space,answering an open question arisen by Dye.Finally,we give a description for Fuglede-Kadison determinant preserving maps on the positive cone of a finite von Neumann algebra and improve Gaal and Nayak’s work on this topic.展开更多
For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(...For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).展开更多
We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-...We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.展开更多
基金supported by Louisiana Christian University Carolyn and Adams Dawson Professorship Fund(2206251515302)the second named author was supported by the NSFC(Grant No.11101220)the Fundamental Research Funds for the Central Universities(Grant No.96172373)。
文摘We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We represent weighted geometric mean preserving bijective maps on the positive cones of prime C^(*)-algebras in terms of Jordan *-isomorphisms of the algebras.We also characterize order isomorphisms and orthoisomorphisms of the projection lattice of the von Neumann algebra of all bounded linear operators on a Hilbert space,answering an open question arisen by Dye.Finally,we give a description for Fuglede-Kadison determinant preserving maps on the positive cone of a finite von Neumann algebra and improve Gaal and Nayak’s work on this topic.
基金partially supported by the NSF of China(11671314)partially supported by the NSF of China(12171251)。
文摘For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).
文摘We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.