A note on the spaces $L_{p}$ for $0<p\leq 1$
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- by N. J. Kalton
- Proc. Amer. Math. Soc. 56 (1976), 199-202
- DOI: https://doi.org/10.1090/S0002-9939-1976-0438103-4
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Abstract:
It is shown that there is no Hausdorff vector topology $\rho$ on the space ${L_p}$ (where $0 < p \leqslant 1$) such that the unit ball of ${L_p}$ is relatively compact for the topology $\rho$.References
- C. Bessaga and A. Pełczyński, On extreme points in separable conjugate spaces, Israel J. Math. 4 (1966), 262–264. MR 211244, DOI 10.1007/BF02771641 I. M. Gelfand, Abstrakte Functionen und lineare Operatoren, Mat. Sb. 4 (46) (1938), 235-286.
- N. J. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402–412. MR 294558, DOI 10.1007/BF02771728
- N. J. Kalton and J. H. Shapiro, An $F$-space with trivial dual and non-trivial compact endomorphisms, Israel J. Math. 20 (1975), no. 3-4, 282–291. MR 402451, DOI 10.1007/BF02760333
- I. Labuda, A generalization of Kalton’s theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 509–510 (English, with Russian summary). MR 323990
- I. Namioka, Neighborhoods of extreme points, Israel J. Math. 5 (1967), 145–152. MR 221271, DOI 10.1007/BF02771100
- Philippe Turpin, Opérateurs linéaires entre espaces d’Orlicz non localement convexes, Studia Math. 46 (1973), 153–165 (French). MR 343010, DOI 10.4064/sm-46-2-153-165
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 199-202
- MSC: Primary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1976-0438103-4
- MathSciNet review: 0438103