On the uniform convexity of $L^p$
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- by Harald Hanche-Olsen PDF
- Proc. Amer. Math. Soc. 134 (2006), 2359-2362
Abstract:
We present a short, direct proof of the uniform convexity of $L^p$ spaces for $1<p<\infty$.References
- James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, DOI 10.1090/S0002-9947-1936-1501880-4
- Olof Hanner, On the uniform convexity of $L^p$ and $l^p$, Ark. Mat. 3 (1956), 239–244. MR 77087, DOI 10.1007/BF02589410
- J. R. Ringrose, A note on uniformly convex spaces, J. London Math. Soc. 34 (1959), 92. MR 100215, DOI 10.1112/jlms/s1-34.1.92
- Keith Ball, Eric A. Carlen, and Elliott H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent. Math. 115 (1994), no. 3, 463–482. MR 1262940, DOI 10.1007/BF01231769
Additional Information
- Harald Hanche-Olsen
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway
- ORCID: 0000-0001-7643-5869
- Email: hanche@math.ntnu.no
- Received by editor(s): March 9, 2005
- Published electronically: February 6, 2006
- Communicated by: Jonathan M. Borwein
- © Copyright 2006 Harald Hanche-Olsen
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2359-2362
- MSC (2000): Primary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-06-08366-3
- MathSciNet review: 2213709