Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity
نویسندگان
چکیده
منابع مشابه
Automatic Continuity and Weighted Composition Operators between Spaces of Vector-valued Differentiable Functions
Let E and F be Banach spaces. It is proved that if Ω and Ω are open subsets of R and R , respectively, and T is a linear biseparating map between two spaces of differentiable functions A(Ω, E) and A(Ω, F ), then p = q, n = m, and there exist a diffeomorphism h of class C from Ω onto Ω, and a map J : Ω → L(E, F ) of class s−C such that for every y ∈ Ω and every f ∈ A(Ω, E), (Tf)(y) = (Jy)(f(h(y)...
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It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y, F ) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y ; in particular we find remarkable differences with respect to t...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2004
ISSN: 0001-8708
DOI: 10.1016/j.aim.2003.09.007