Additive mappings on C ∗ -algebras sub-preserving absolute values of products
Tóm tắt
Let
be a
-algebra of real rank zero and
be a
-algebra with unit I. It is shown that if
is an additive mapping which satisfies
for every
and
for some
with
, then the restriction of mapping ϕ to
is a Jordan homomorphism, where
denotes the set of all self-adjoint elements. We will also show that if ϕ is surjective preserving the product and an absolute value, then ϕ is a
-linear or
-antilinear ∗-homomorphism on
. MSC:47B49, 46L05, 47L30.
Tài liệu tham khảo
Aupetit B, du Toit Mouton H: Spectrum preserving linear mappings in Banach algebras. Stud. Math. 1994, 109: 91–100.
Brešar M: Commuting traces of biadditive mappings, commutativity-preserving, mappings and Lie mappings. Trans. Am. Math. Soc. 1993, 335: 525–546.
Chan GH, Lim MH: Linear preservers on powers of matrices. Linear Algebra Appl. 1992, 162–164: 615–626.
Choi MD, Jafarian AA, Radjavi H: Linear maps preserving commutativity. Linear Algebra Appl. 1987, 87: 227–241.
Jafarian AA, Sourour AR: Spectrum-preserving linear maps. J. Funct. Anal. 1986, 66: 255–261. 10.1016/0022-1236(86)90073-X
Gudder S, Nagy G: Quentially independent effects. Proc. Am. Math. Soc. 2002, 130: 1125–1130. 10.1090/S0002-9939-01-06194-9
Kadison RV, Ringrose JR: Fundamentals of the Theory of Operator Algebras: Elementary Theory. Academic Press, New York; 1997.
Kadison RV, Ringrose JR: Fundamentals of the Theory of Operator Algebras: Advanced Theory. Academic Press, Orlando; 1997.
Li CK, Tsing NK: Linear preserver problems: a brief introduction and some special techniques. Linear Algebra Appl. 1992, 162–164: 217–235.
Molnár L:Two characterisations of additive *-automorphisms of B(H) . Bull. Aust. Math. Soc. 1996, 53: 391–400. 10.1017/S0004972700017147
Molnár L: Multiplicative Jordan triple isomorphisms on the selfadjoint elements of von Neuman algebras. Linear Algebra Appl. 2006, 419: 586–600. 10.1016/j.laa.2006.06.007
Omladič M: On operators preserving commutativity. J. Funct. Anal. 1986, 66: 105–122. 10.1016/0022-1236(86)90084-4
Omladič M, Šemrl P: Linear mappings that preserve potent operators. Proc. Am. Math. Soc. 1995, 123: 1069–1074.
Radjabalipour M: Additive mappings on von Neumann algebras preserving absolute values. Linear Algebra Appl. 2003, 368: 229–241.
Radjabalipour M, Seddighi K, Taghavi Y: Additive mappings on operator algebras preserving absolute values. Linear Algebra Appl. 2001, 327: 197–206. 10.1016/S0024-3795(00)00338-4
Śemrl P: Linear mappings preserving square-zero matrices. Bull. Aust. Math. Soc. 1993, 48: 365–370. 10.1017/S0004972700015811
Taghavi A:Additive mappings on C ∗ -algebras preserving absolute values. Linear Multilinear Algebra 2012, 60(1):33–38. 10.1080/03081087.2010.533271