Abstract
We prove a Banach–Stone type theorem for surjective linear isometries of quaternion-valued continuous function spaces.
Similar content being viewed by others
References
Araujo J., Font J.J.: Linear isometries between subspaces of continuous fuctions. Trans. Am. Math. Soc. 349, 413–428 (1997)
Al-Halees H., Fleming R.J.: Extreme point methods and Banach-Stone theorem. J. Aust. Math. Soc. 75, 125–143 (2003)
Behrends, E.: M-structures and the Banach-Stone theorem, Lect. Notes in Math. vol. 736. Springer (1979)
Botelho F., Fleming R.J., Jamison J.: Extreme points and isometries on vector-valued Lipschitz spaces. J. Math. Anal. Appl. 381, 821–832 (2011)
Cambern M.: A Holszynski theorem for spaces of continuous vector-valued functions. Stud. Math. 63, 213–217 (1978)
Dunford N., Schwarz J.: Linear operators, vol. 1, General Theory. Interscience, New York (1958)
Ebbinghaus, H.D.: Numbers, GTM, vol 123. Springer (1990)
Engelking, H.D.: Theory of Dimensions, Finite and Infinite, Sigma Ser. in Pure Math., vol. 10. Helderman Verlag (1995)
Fleming, H.D., Jamison, H.D.: Isometries on Banach spaces, vol. 1, Function Spaces. Monographs and Surveys in Pure and Applied Math., vol. 129. Chapman & Hall/CRC, Boca Raton (2003)
Fleming, R., Jamison, R.: Isometries on Banach spaces vol. 2, Vector-valued function spaces. Monographs and Surveys in Pure and Applied Math., vol. 138. Chapman & Hall/CRC, Boca Raton (2008)
Garrido M.I., Jaramillo M.I.: Variations on the Banach Stone theorem. Extracta Mathematicae 17, 351–383 (2002)
Holszynski W.: Continuous mappings induced by isometries of spaces of continuous functions. Stud. Math. 26, 133–136 (1966)
Jarosz K., Pathak V.D.: Isometries between function spaces. Trans. Am. Math. Soc. 305, 193–206 (1988)
Jarosz, K., Pathak, V.D.: Isometries and small bound isomorphisms of function spaces, in Function Spaces, Edwardsville Il 1990, Lecture Notes in Pure Appl. Math., vol. 136, pp. 241–271. Marcel-Dekker (1992)
Jarosz K.: Function representation of a noncommutative uniform algebra. Proc. Am. Math. Soc. 136, 605–611 (2008)
Kadison R.: Isometries of operator algebras. Ann. Math. 54, 325–338 (1951)
Kawamura K.: Linear surjective isometries between vector-valued function spaces. J. Aust. Math. Soc. 100, 349–373 (2016)
Kawamura, K., Miura T.: Real-linear surjective isometries between function spaces (preprint)
Koshimizu H., Miura T., Takagi H., Takahasi S.-E.: Real-linear isometries between subspaces of continuous functions. J. Math. Anal. Appl. 413, 229–241 (2014)
Lau K.-S.: A representation theorem for isometris of C(X,E). Pac. J. Math. 60, 229–233 (1975)
Megginson, R.: An introduction to Banach space theory, GTM, vol. 183. Springer (1998)
Miura T.: Surjective isometries between function spaces. Contemp. Math. 645, 231–239 (2015)
Novinger W.: Linear isometries of subspaces of spaces of continuous functions. Stud. Math. 53, 273–276 (1975)
Rudin, W.: Real and Complex Analysis,3rd edn. McGraw-Hill (1986)
Spanier, E.H.: Algebraic topology. McGraw-Hill (1966)
Väisälä J.: A proof of the Mazur–Ulam theorem. Am. Math. Mon. 110(7), 633–635 (2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
The author is supported by JSPS KAKENHI Grant Number 26400080.
Rights and permissions
About this article
Cite this article
Kawamura, K. Banach–Stone Theorem for Quaternion- Valued Continuous Function Spaces. Mediterr. J. Math. 13, 4745–4761 (2016). https://doi.org/10.1007/s00009-016-0773-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-016-0773-x