Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.

Abstract

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $T : A \longrightarrow B$,  where $A$ and $B$ are complex function spaces on compact Hausdorff spaces $X$ and $Y$, respectively, whenever ${\rm ER}\left (A, X\right ) = {\rm Ch}\left (A, X\right )$ and ${\rm ER}\left (B, Y\right ) = {\rm Ch}\left (B, Y\right )$. Next, we give a description of $T$ whenever $A$ and $B$ are complex function algebras  and $T$ does not assume to be unit-preserving.

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References
[1] D. Alimohammadi and T. Ghasemi Honary, Choquet and Shilov boundaries, peak sets and peak points for real Banach function algebras, Journal of Function Spaces and Applications, 2013 (2013), pp. 1-9.

[2] A. Browder, Introduction to Function Algebras, W. A. Benjamin, New York, 1969.

[3] A.J. Ellis, Real characterization of function algebras amongst function spaces, Bull. London Math. Soc., 22 (1990), pp. 381-385.

[4] A. Jamshidi and F. Sady, Real-linear isometries between certain subspaces of continuous functions, Cent. Eur. J. Math., 11 (2013), pp. 2034-2043.

[5] E. Kaniuth, A Course in Commutative Banach Algebras, Springer, 2009.

[6] S.H. Kulkarni and B.V. Limaye, Boundaries and Choquet sets for real subspaces of C(X), Mathematica Japonica, 51 (2000), pp. 199-212.

[7] S.H. Kulkarni and B.V. Limaye, Real Function Algebras, Marcel Dekker, New York, 1992.

[8] T. Miura, Real-linear isometries between function algebras, Cent. Eur. J. Math., 9 (2011), pp. 778-788.

[9] D.R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math., 13 (1963), pp. 1387-1399.