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Maps preserving common zeros between subspaces of vector-valued continuous functions. (English) Zbl 1220.47042
Suppose that X and Y are metric spaces and E and F are normed vector spaces. Denote by C(X,E) and C(Y,F) the corresponding spaces of continuous functions and by A(X,E) and A(Y,F) subspaces of C(X,E) and C(Y,F), respectively. The zero set of a function fC(X,E) is defined as Z(f)=xX:f(x)=0. The paper under review provides a complete characterization of linear and bijective maps T:A(X,E)A(Y,F) such that Z(f)Z(g) if and only if Z(fg) for any f,gA(X,E)· An application to automatic continuity is included.
47B38Operators on function spaces (general)
46E40Spaces of vector- and operator-valued functions
46H40Automatic continuity
47B33Composition operators
[1]Araujo J.: Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity. Adv. Math. 187, 488–520 (2004) · Zbl 1073.47031 · doi:10.1016/j.aim.2003.09.007
[2]Araujo J., Dubarbie L.: Biseparating maps between Lipschitz function spaces. J. Math. Anal. Appl. 357, 191–200 (2009) · Zbl 1169.47024 · doi:10.1016/j.jmaa.2009.03.065
[3]Cao J., Reilly I., Xiong H.: A lattice-valued Banach-Stone theorem. Acta Math. Hungar. 98, 103–110 (2003) · Zbl 1027.46025 · doi:10.1023/A:1022861506272
[4]Chen J.X., Chen Z.L., Wong N.C.: A Banach-Stone theorem for Riesz isomorphisms of Banach lattices. Proc. Am. Math. Soc. 136, 3869–3874 (2008) · Zbl 1160.46026 · doi:10.1090/S0002-9939-08-09582-8
[5]Dubarbie, L.: Separating maps between spaces of vector-valued absolutely continuous functions. Canad. Math. Bull. (to appear). arXiv:0906.1633v1
[6]Ercan Z., Önal S.: Banach-Stone theorem for Banach lattice valued continuous functions. Proc. Am. Math. Soc. 135, 2827–2829 (2007) · Zbl 1127.46026 · doi:10.1090/S0002-9939-07-08788-6
[7]Ercan Z., Önal S.: The Banach-Stone theorem revisited. Topol. Appl. 155, 1800–1803 (2008) · Zbl 1166.46309 · doi:10.1016/j.topol.2008.05.018
[8]Hewitt E., Stromberg K.: Real and Abstract Analysis. Springer, New York (1975)
[9]Jiménez-Vargas A., Morales Campoy A., Villegas-Vallecillos M.: The uniform separation property and Banach-Stone theorems for lattice-valued Lipschitz functions. Proc. Am. Math. Soc. 137, 3769–3777 (2009) · Zbl 1202.46043 · doi:10.1090/S0002-9939-09-09941-9
[10]Leung, D.H., Tang, W.K.: Banach-Stone theorems for maps preserving common zeros. Positivity. doi: 10.1007/s11117-008-0002-3
[11]Miao X., Cao J., Xiong H.: Banach-Stone theorems and Riesz algebras. J. Math. Anal. Appl. 313, 177–183 (2006) · Zbl 1102.46017 · doi:10.1016/j.jmaa.2005.08.050
[12]Weaver N.: Lipschitz Algebras. World Scientific Publishing, Singapore (1999)