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POSITIVE LINEAR OPERATORS IN C*-ALGEBRAS
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 Title & Authors
POSITIVE LINEAR OPERATORS IN C*-ALGEBRAS
Park, Choon-Kil; An, Jong-Su;
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 Abstract
It is shown that every almost positive linear mapping h : of a Banach *-algebra to a Banach *-algebra is a positive linear operator when h(rx) = rh(x) (r > 1) holds for all , and that every almost linear mapping h : of a unital C*-algebra to a unital C*-algebra is a positive linear operator when h() = h()*h(y) holds for all unitaries , all , and all n = 0, 1, 2, ..., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : of a unital C*-algebra A to a unital C*-algebra is a positive linear operator. It is applied to investigate states, center states and center-valued traces.
 Keywords
C*-algebra;positive linear operator;state;Hyers-Ulam-Rassias stability;linear functional equation;
 Language
English
 Cited by
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