Geometry of Lebesgue-Bochner function spaces—smoothness
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- by I. E. Leonard and K. Sundaresan PDF
- Bull. Amer. Math. Soc. 79 (1973), 546-549
References
- S. Bochner and A. E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Ann. of Math. (2) 39 (1938), no. 4, 913–944. MR 1503445, DOI 10.2307/1968472
- Robert Bonic and John Frampton, Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877–898. MR 0198492
- Henri Cartan, Differential calculus, Hermann, Paris; Houghton Mifflin Co., Boston, Mass., 1971. Exercises by C. Buttin, F. Rideau and J. L. Verley; Translated from the French. MR 0344032
- Dennis F. Cudia, The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284–314. MR 163143, DOI 10.1090/S0002-9947-1964-0163143-9 5. M. M. Day, Normed linear spaces, 2nd rev. ed., Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
- J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
- N. Dinculeanu, Vector measures, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
- R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 0221256
- Gottfried Köthe, Topologische lineare Räume. I, Die Grundlehren der mathematischen Wissenschaften, Band 107, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0130551, DOI 10.1007/978-3-662-22555-4
- E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 1 (1950), 402–408. MR 36448, DOI 10.1090/S0002-9939-1950-0036448-5
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- Kondagunta Sundaresan, Smooth Banach spaces, Math. Ann. 173 (1967), 191–199. MR 218876, DOI 10.1007/BF01361710
Additional Information
- Journal: Bull. Amer. Math. Soc. 79 (1973), 546-549
- MSC (1970): Primary 46E40, 28A45; Secondary 58C20, 28A15
- DOI: https://doi.org/10.1090/S0002-9904-1973-13195-7
- MathSciNet review: 0326376