Linear orthogonality preservers of Hilbert $C^{*}$-modules over $C^{*}$-algebras with real rank zero
نویسندگان
چکیده
منابع مشابه
Linear Orthogonality Preservers of Hilbert C∗-modules over C∗-algebras with Real Rank Zero
Let A be a C∗-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ : E → F is a linear map preserving orthogonality, i.e., 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u ∈M(A) such that 〈θ(x), θ(y)〉 = u〈x, y〉 (x...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11260-2