Maps preserving common zeros between subspaces of vector-valued continuous functions

2009/10/13 by Luis Dubarbie, Dubarbie, Luis
Mathematics · #46E15 #46E40 #46H40 #47B33 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E15 #msc:46E40 #msc:46H40 #msc:47B33 #msc:47B38

paper · pdf · doi:10.48550/arxiv.0910.2358

10 pages

arxiv created 2009/10/13 · arxiv updated 2009/12/01

Abstract

For metric spaces X and Y, normed spaces E and F, and certain subspaces A(X,E) and A(Y,F) of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps T:A(X,E)→ A(Y,F) preserving common zeros, that is, maps satisfying the property \setcounterequation15 Z(f)∩ Z(g)≠ ∅ \Longleftrightarrow Z(Tf)∩ Z(Tg)≠ ∅ for any f,g∈ A(X,E), where Z(f)=\x∈ X:f(x)=0\. Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (\refdub) is derived.

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