Abstract
In this paper we describe, under certain assumptions, surjective diameter preserving mappings when defined between function spaces, not necessarily algebras, thus extending most of the previous results for these operators. We provide an example which shows that our assumptions are not redundant.
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Aizpuru, A., Rambla, F.: There’s something about the diameter. J. Math. Anal. Appl. 330, 949–962 (2007)
Aizpuru, A., Tamayo, M.: Linear bijections which preserve the diameter of vector-valued maps. Linear Algebra Appl. 424, 371–377 (2007)
Aizpuru, A., Tamayo, M.: On diameter preserving linear maps. J. Korean Math. Soc. 45, 197–204 (2008)
Aizpuru, A., Rambla, F.: Diameter preserving linear bijections and \(C_0(L)\) spaces. Bull. Belg. Math. Soc. Simon Stevin 17, 377–383 (2010)
Asimow, L., Ellis, A.J.: Convexity theory and its applications in functional analysis. Academic, London (1980)
Bacak, M.: Unique decomposition property and extreme points. Rocky Mt. J. Math. 39, 1397–1402 (2009)
Barnes, B.A., Roy, A.K.: Diameter preserving maps on various classes of function spaces. Studia Math. 153, 127–145 (2002)
Cabello, F.: Sánchez, Diameter preserving linear maps and isometries. Arch. Math. 73, 373–379 (1999)
Sánchez, F.C.: Diameter preserving linear maps and isometries II. Proc. Indian Acad. Sci. (Math. Sci.) 110, 205–211 (2000)
Cengiz, B.: On extremely regular function spaces. Pac. J. Math. 49, 335–338 (1973)
Curtis, P. C.: Topics in Banach spaces of continuous functions. Lecture Notes Series, No. 25. Aarhus Universitet, Matematisk institut, Aarhus (1970)
Font, J.J., Hosseini, M.: Diameter preserving mappings between function algebras. Taiwan. J. Math. 15, 1487–1495 (2011)
Font, J.J., Sanchis, M.: A characterization of locally compact spaces with homeomorphic one-point compactifications. Topol. Appl. 121, 91–104 (2002)
Font, J.J., Sanchis, M.: Extreme points and the diameter norm. Rocky Mt. J. Math. 34, 1325–1331 (2004)
González, F., Uspenskij, V.V.: On homomorphisms of groups of integer-valued functions. Extr. Math. 14, 19–29 (1999)
Győry, M., Molnár, L.: Diameter preserving linear bijections of \(C(X)\). Arch. Math. 71, 301–310 (1998)
Leibowitz, G.M.: Lectures on complex function algebras. Scott Foresman and Company, Glenview, Ill (1970)
Rao, T.S.S.R.K., Roy, A.K.: Diameter preserving linear bijections of function spaces. J. Aust. Math. Soc. 70, 323–335 (2001)
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Research of J.J. Font was partially supported by Universitat Jaume I (Projecte P1\(\cdot \)1B2014-35) and Generalitat Valenciana (Projecte AICO/16/030).
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Hosseini, M., Font, J.J. Diameter preserving maps on function spaces. Positivity 21, 875–883 (2017). https://doi.org/10.1007/s11117-016-0438-9
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DOI: https://doi.org/10.1007/s11117-016-0438-9