Abstract
The Banach spaces Lipa (S, Δ), lipa (S, Δ), Lipa (S, Δ;s 0) and lipa (S, Δ;s 0) of Lipschitz functions are defined. We shall identify the extreme points of the unit balls in their corresponding dual spaces and make use of them to present a complete characterization of the isometries between these function spaces.
Similar content being viewed by others
References
R. Bonic, J. Frampton and A. Tromba,Δ-manifolds, J. Functional Analysis3 (1969), 310–320.
K. de Leeuw,Banach spaces of Lipschitz functions, Studia Math.21 (1961), 55–66.
N. Dunford and J. Schwartz,Linear Operators, Vol. I, Interscience, New York, 1958.
J. Johnson,Banach spaces of Lipschitz functions and vector valued Lipschitz functions, Trans. Amer. Math. Soc.148 (1970), 147–169.
J. Johnson,Lipschitz spaces, Pacific J. Math.51 (1974), 177–186.
J. Johnson,A note on Banach spaces of Lipschitz functions, Pacific J. Math.58 (1975), 475–482.
S. Kislyakov,Sobelev imbedding operators and the nonisomorphism of certain Banach spaces, Functional Anal. Appl.9 (1975), 290–294.
D. Sherbert,The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc.111 (1964), 240–272.
A. Tromba,On the isometries of spaces of Hölder continuous functions, Studia Math.57 (1976), 199–208.
Author information
Authors and Affiliations
Additional information
This paper is a part of the author’s M.Sc. thesis which was prepared under the guidance of Dr. Y. Benyamini.
Rights and permissions
About this article
Cite this article
Mayer-Wolf, E. Isometries between Banach spaces of Lipschitz functions. Israel J. Math. 38, 58–74 (1981). https://doi.org/10.1007/BF02761849
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761849