A Banach space characterization of purely atomic measure spaces
HTML articles powered by AMS MathViewer
- by R. R. Phelps PDF
- Proc. Amer. Math. Soc. 12 (1961), 447-452 Request permission
References
- Leon Alaoglu, Weak topologies of normed linear spaces, Ann. of Math. (2) 41 (1940), 252–267. MR 1455, DOI 10.2307/1968829
- Mahlon M. Day, Normed linear spaces, Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0094675
- Jean Dieudonné, Sur les espaces $L^{1}$, Arch. Math. 10 (1959), 151–152 (French). MR 105016, DOI 10.1007/BF01240778 I. Gelfand, Abstrakte Funktionen und lineare Operatoren, Mat. Sb. vol. 4 (1938) pp. 235-284.
- Paul R. Halmos, The range of a vector measure, Bull. Amer. Math. Soc. 54 (1948), 416–421. MR 24963, DOI 10.1090/S0002-9904-1948-09020-6
- Shizuo Kakutani, Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994–1024. MR 5778, DOI 10.2307/1968778
- Shizuo Kakutani, Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523–537. MR 4095, DOI 10.2307/1968915
- A. R. Lovaglia, Locally uniformly convex Banach spaces, Trans. Amer. Math. Soc. 78 (1955), 225–238. MR 66558, DOI 10.1090/S0002-9947-1955-0066558-7
Additional Information
- © Copyright 1961 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 12 (1961), 447-452
- MSC: Primary 46.35
- DOI: https://doi.org/10.1090/S0002-9939-1961-0140934-4
- MathSciNet review: 0140934