Orthogonal forms and orthogonality preservers on real function algebras revisited
نویسندگان
چکیده
منابع مشابه
Linear Orthogonality Preservers of Standard Operator Algebras
In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...
متن کاملLinear 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...
متن کاملLinear Orthogonality Preservers of Hilbert Bundles
A C-linear map θ (not necessarily bounded) between two Hilbert C-modules is said to be ‘orthogonality preserving’ if 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We prove that if θ is an orthogonality preserving map from a full Hilbert C0()-module E into another Hilbert C0()-module F that satisfies a weaker notion of C0()-linearity (called ‘localness’), then θ is bounded and there exists φ ∈ Cb()+...
متن کاملLinear Orthogonality Preservers of Hilbert Modules
We verify in this paper that the linearity and orthogonality structures of a (not necessarily local trivial) Hilbert bundle over a locally compact Hausdorff space Ω determine its unitary structure. In fact, as Hilbert bundles over Ω are exactly Hilbert C0(Ω)-modules, we have a more general set up. A C-linear map θ (not assumed to be bounded) between two Hilbert C∗-modules is said to be “orthogo...
متن کاملLinear Orthogonality Preservers of Hilbert C∗-modules
We show in this paper that the module structure and the orthogonality structure of a Hilbert C∗-module determine its inner product structure. Let A be a C∗-algebra, and E and F be Hilbert A-modules. Assume Φ : E → F is an A-module map satisfying 〈Φ(x),Φ(y)〉A = 0 whenever 〈x, y〉A = 0. Then Φ is automatically bounded. In case Φ is bijective, E is isomorphic to F . More precisely, let JE be the cl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2016
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2016.1186147