Topological conditions for bound-2 isomorphisms of C(X)

• Autorzy: H. B. Cohen , C.-H. Chu
• Języki publikacji: EN

Abstrakty

EN

We establish the topological relationship between compact Hausdorff spaces X and Y equivalent to the existence of a bound-2 isomorphism of the sup norm Banach spaces C(X) and C(Y).

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 54C35: Function spaces
• 54C08: Weak and generalized continuity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 113
• Numer: 1
• Strony: 1-24

Daty

wydano

1995

otrzymano

1992-11-20

poprawiono

1993-10-25

Twórcy

autor

H. B. Cohen

• Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.

autor

C.-H. Chu

• Goldsmiths' College, University of London, London SE14, England

Bibliografia

• [1] D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205-210.
• [2] E. Behrends, M-structure and the Banach-Stone Theorem, Lecture Notes in Math. 736, Springer, 1979.
• [3] Y. Benyamini, Near isometries in the class of $L^1$-preduals, Israel J. Math. 20 (1975), 275-291.
• [4] M. Cambern, A generalized Banach-Stone Theorem, Proc. Amer. Math. Soc. 17 (1966), 396-400.
• [5] M. Cambern, On isomorphisms with small bounds, ibid. 18 (1967), 1062-1066.
• [6] M. Cambern, On $L^1$ isomorphisms, ibid. 78 (1980), 227-229.
• [7] M. Cambern, Isomorphisms of spaces of norm continuous functions, Pacific J. Math. 116 (1985), 243-254.
• [8] M. Cambern and P. Greim, The bidual of C(X,E), Proc. Amer. Math. Soc. 85 (1982), 53-583.
• [9] M. Cambern and P. Greim, The dual of a space of vector measures, Math. Z. 180 (1982), 373-378.
• [10] H. B. Cohen, A bound-two isomorphism for C(X) Banach spaces, Proc. Amer. Math. Soc. 50 (1975), 215-217.
• [11] H. B. Cohen, A second-dual method for C(X) isomorphism, J. Funct. Anal. 23 (1975), 107-118.
• [12] C. H. Chu and H. B. Cohen, Isomorphisms of spaces of continuous affine functions, Pacific J. Math. 155 (1992), 71-85.
• [13] J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2, (1951), 151-182.
• [14] H. Gordon, The maximal ideal space of a ring of measurable functions, Amer. J. Math. 88 (1966), 827-843.
• [15] J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107 (1963), 38-43.
• [16] K. Jarosz, Small isomorphisms of C(X,E) spaces, Pacific J. Math. 138 (1989), 295-315.
• [17] S. Kakutani, Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann. of Math. 42 (1941), 523-537.
• [18] J. L. Kelley, Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), 323-326.
• [19] J. Lamperti, On the isometries of certain function spaces, Pacific J. Math. 8 (1958), 459-466.