Topics in Banach Space Theory pp 77-107 | Cite as
Banach Spaces of Continuous Functions
Chapter
First Online:
Abstract
We are now going to shift our attention from sequence spaces to spaces of functions, and we start in this chapter by considering spaces of type \(\mathcal{C}(K)\).
References
- 5.F. Albiac, E. Briem, Representations of real Banach algebras. J. Aust. Math. Soc. 88, 289–300 (2010)MathSciNetCrossRefMATHGoogle Scholar
- 7.F. Albiac, N.J. Kalton, A characterization of real \(\mathcal{C}\)(K)-spaces. Am. Math. Mon. 114 (8), 737–743 (2007)MathSciNetMATHGoogle Scholar
- 12.D. Amir, On isomorphisms of continuous function spaces. Isr. J. Math. 3, 205–210 (1965)MathSciNetCrossRefMATHGoogle Scholar
- 14.R. Arens, Representation of *-algebras. Duke Math. J. 14, 269–282 (1947)MathSciNetCrossRefMATHGoogle Scholar
- 18.S. Banach, Théorie des opérations linéaires. Monografje Matematyczne (Warszawa, 1932)Google Scholar
- 25.C. Bessaga, A. Pełczyński, Spaces of continuous functions IV: on isomorphical classification of spaces of continuous functions. Stud. Math. 19, 53–62 (1960)MathSciNetMATHGoogle Scholar
- 27.K. Borsuk, Über Isomorphie der Funktionalräume. Bull. Int. Acad. Pol. Sci. 1–10 (1933)Google Scholar
- 39.M. Cambern, A generalized Banach–Stone theorem. Proc. Am. Math. Soc. 17, 396–400 (1966)MathSciNetCrossRefMATHGoogle Scholar
- 51.H.B. Cohen, A bound-two isomorphism between C(X) Banach spaces. Proc. Am. Math. Soc. 50, 215–217 (1975)MathSciNetMATHGoogle Scholar
- 52.J.B. Conway, A Course in Functional Analysis. Graduate Texts in Mathematics, vol. 96 (Springer, New York, 1985)Google Scholar
- 58.L. de Branges, The Stone–Weierstrass theorem. Proc. Am. Math. Soc. 10, 822–824 (1959)MathSciNetCrossRefMATHGoogle Scholar
- 71.J. Dixmier, Sur certains espaces considérés par M. H. Stone. Summa Bras. Math. 2, 151–182 (1951) (French)Google Scholar
- 96.I. Fredhom, Sur une classe d’équations fonctionelles. Acta Math. 27, 365–390 (1903)MathSciNetCrossRefGoogle Scholar
- 110.D.B. Goodner, Projections in normed linear spaces. Trans. Am. Math. Soc. 69, 89–108 (1950)MathSciNetCrossRefMATHGoogle Scholar
- 113.W.T. Gowers, A solution to Banach’s hyperplane problem. Bull. Lond. Math. Soc. 26 (6), 523–530 (1994)MathSciNetCrossRefMATHGoogle Scholar
- 169.J.L. Kelley, Banach spaces with the extension property. Trans. Am. Math. Soc. 72, 323–326 (1952)MathSciNetCrossRefMATHGoogle Scholar
- 179.P. Koszmider, Banach spaces of continuous functions with few operators. Math. Ann. 330, 151–183 (2004)MathSciNetCrossRefMATHGoogle Scholar
- 220.A.A. Miljutin, Isomorphism of the spaces of continuous functions over compact sets of the cardinality of the continuum. Teor. Funkciĭ Funkcional. Anal. Priložen. Vyp. 2, 150–156 (1966) (1 foldout) (Russian)Google Scholar
- 225.L. Nachbin, On the Han–Banach theorem. An. Acad. Bras. Cienc. 21, 151–154 (1949)MathSciNetMATHGoogle Scholar
- 236.T.W. Palmer, Banach Algebras and the General Theory of ∗ -Algebras. Vol. I. Encyclopedia of Mathematics and Its Applications, vol. 49 (Cambridge University Press, Cambridge, 1994)Google Scholar
- 239.A. Pełczyński, On the isomorphism of the spaces m and M. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 6, 695–696 (1958)MathSciNetMATHGoogle Scholar
- 262.G. Plebanek, A construction of a Banach space C(K) with few operators. Topol. Appl. 143 (1–3), 217–239 (2004)MathSciNetCrossRefMATHGoogle Scholar
- 266.T.J. Ransford, A short elementary proof of the Bishop–Stone–Weierstrass theorem. Proc. Camb. Philol. Soc. 96 (2), 309–311 (1984)MathSciNetCrossRefMATHGoogle Scholar
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