Geometry of Lebesgue-Bochner function spaces—smoothness
Authors:
I. E. Leonard and K. Sundaresan
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
Full-text PDF
References | Similar Articles | Additional Information
- 1. 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, https://doi.org/10.2307/1968472
- 2. R. Bonic and J. Frampton, Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877-898. MR 33 #6647. MR 198492
- 3. H. Cartan, Differential calculus, Hermann, Paris, 1971. MR 344032
- 4. D. F. Cudia, The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284-314. MR 29 #446. MR 163143
- 5. M. M. Day, Normed linear spaces, 2nd rev. ed., Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
- 6. J. Dieudonné, Foundations of modern analysis, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074. MR 120319
- 7. N. Dinculeanu, Vector measures, Internat. Ser. of Monographs in Pure and Appl. Math., vol. 95, Pergamon Press, London, 1967. MR 34 #601lb. MR 206190
- 8. R. E. Edwards, Functional analysis, theory and applications, Holt, Rinehart and Winston, New York, 1965. MR 36 #4308. MR 221256
- 9. G. Köthe, Topologische linear Räume. I, Die Grundlehren der math. Wissenschaften, Band 107, Springer-Verlag, Berlin, 1966; English transl., Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1969. MR 33 # 3069; MR 40 # 1750. MR 130551
- 10. E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 1 (1950), 402-408. MR 12, 110. MR 36448
- 11. E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N.J., 1971. MR 304972
- 12. K. Sundaresan, Smooth Banach spaces, Math. Ann. 173 (1967), 191-199. MR 36 # 1960. MR 218876
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 46E40, 28A45, 58C20, 28A15
Retrieve articles in all journals with MSC (1970): 46E40, 28A45, 58C20, 28A15
Additional Information
DOI:
https://doi.org/10.1090/S0002-9904-1973-13195-7
