The Choquet representation in the complex case
HTML articles powered by AMS MathViewer
- by R. R. Phelps PDF
- Bull. Amer. Math. Soc. 83 (1977), 299-312
References
- Erik M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 57, Springer-Verlag, New York-Heidelberg, 1971. MR 0445271, DOI 10.1007/978-3-642-65009-3
- Eggert Briem, Interpolation in subspaces $C(X)$, J. Functional Analysis 12 (1973), 1–12. MR 0343001, DOI 10.1016/0022-1236(73)90086-4 3. G. Choquet, Lectures on analysis, Vol. II, Benjamin, New York, 1969. MR 40 #3253; 44, p. 1630.
- Gustave Choquet, Frontière-module et représentation intégrale, Séminaire Choquet, 11e-12e années (1971–1973), Initiation à l’analyse, Exp. No. 8, Secrétariat Mathématique, Paris, 1973, pp. 4 (French). MR 0477766 5. G. Choquet, Frontières et représentations intégrales relatives à un espace de fonctions continues á valeurs complexes, 1973 (handwritten manuscript).
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Edward G. Effros, On a class of complex Banach spaces, Illinois J. Math. 18 (1974), 48–59. MR 328548
- Richard Fuhr and R. R. Phelps, Uniqueness of complex representing measures on the Choquet boundary, J. Functional Analysis 14 (1973), 1–27. MR 0361741, DOI 10.1016/0022-1236(73)90027-x
- Bent Hirsberg, Représentations intégrales des formes linéaires complexes, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1222–A1224 (French). MR 296668
- B. Hirsberg and A. J. Lazar, Complex Lindenstrauss spaces with extreme points, Trans. Amer. Math. Soc. 186 (1973), 141–150. MR 333671, DOI 10.1090/S0002-9947-1973-0333671-7
- Otte Hustad, A norm preserving complex Choquet theorem, Math. Scand. 29 (1971), 272–278 (1972). MR 322490, DOI 10.7146/math.scand.a-11053
- Otte Hustad, Intersection properties of balls in complex Banach spaces whose duals are $L_{1}$ spaces, Acta Math. 132 (1974), no. 3-4, 283–313. MR 388049, DOI 10.1007/BF02392118
- Åsvald Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1–62. MR 430747, DOI 10.1090/S0002-9947-1977-0430747-4
- Åsvald Lima, An application of a theorem of Hirsberg and Lazar, Math. Scand. 38 (1976), no. 2, 325–340. MR 435802, DOI 10.7146/math.scand.a-11639
- Asvald Lima, Complex Banach spaces whose duals are $L_{1}$-spaces, Israel J. Math. 24 (1976), no. 1, 59–72. MR 425584, DOI 10.1007/BF02761429
- L. H. Loomis, Dilations and extremal measures, Advances in Math. 17 (1975), no. 1, 1–13. MR 374866, DOI 10.1016/0001-8708(75)90081-X
- Gunner Hans Olsen, On the classification of complex Lindenstrauss-spaces, Mathematics Preprint Series, No. 16 (1973), Universitetet i Oslo, Matematisk Institutt, Oslo, 1973. MR 0394128
- Gunnar Hans Olsen, On the classification of complex Lindenstrauss spaces, Math. Scand. 35 (1974), 237–258. MR 367626, DOI 10.7146/math.scand.a-11550
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
- Robert R. Phelps, Lectures on Choquet’s theorem, 2nd ed., Lecture Notes in Mathematics, vol. 1757, Springer-Verlag, Berlin, 2001. MR 1835574, DOI 10.1007/b76887
- R. R. Phelps, Integral representations for elements of convex sets, Studies in functional analysis, MAA Stud. Math., vol. 21, Math. Assoc. America, Washington, D.C., 1980, pp. 115–157. MR 589415
- Murali Rao, Measurable selections of representing measures, Quart. J. Math. Oxford Ser. (2) 22 (1971), 571–573. MR 300069, DOI 10.1093/qmath/22.4.571
- Paulette Saab, Représentation intégrale dans des sous-espaces de fonctions à valeurs vectorielles, Séminaire Choquet, 14e année (1974/75), Initiation à l’analyse, Exp. No. 23, Secrétariat Mathématiques, Paris, 1975, pp. 10 (French). MR 0477763
- G. F. Vincent-Smith, Measurable selections of simplicial maximal measures, J. London Math. Soc. (2) 7 (1974), 427–428. MR 336292, DOI 10.1112/jlms/s2-7.3.427
Additional Information
- Journal: Bull. Amer. Math. Soc. 83 (1977), 299-312
- MSC (1970): Primary 28A10, 28A45, 46E15
- DOI: https://doi.org/10.1090/S0002-9904-1977-14243-2
- MathSciNet review: 0435818