@article{CML_2011__3_4_637_0, author = {Aubrun, Guillaume and Nechita, Ion}, title = {The multiplicative property characterizes $\ell _p$ and $L_p$ norms}, journal = {Confluentes Mathematici}, pages = {637--647}, publisher = {World Scientific Publishing Co Pte Ltd}, volume = {3}, number = {4}, year = {2011}, doi = {10.1142/S1793744211000485}, language = {en}, url = {http://archive.numdam.org/articles/10.1142/S1793744211000485/} }
TY - JOUR AU - Aubrun, Guillaume AU - Nechita, Ion TI - The multiplicative property characterizes $\ell _p$ and $L_p$ norms JO - Confluentes Mathematici PY - 2011 SP - 637 EP - 647 VL - 3 IS - 4 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744211000485/ DO - 10.1142/S1793744211000485 LA - en ID - CML_2011__3_4_637_0 ER -
%0 Journal Article %A Aubrun, Guillaume %A Nechita, Ion %T The multiplicative property characterizes $\ell _p$ and $L_p$ norms %J Confluentes Mathematici %D 2011 %P 637-647 %V 3 %N 4 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744211000485/ %R 10.1142/S1793744211000485 %G en %F CML_2011__3_4_637_0
Aubrun, Guillaume; Nechita, Ion. The multiplicative property characterizes $\ell _p$ and $L_p$ norms. Confluentes Mathematici, Tome 3 (2011) no. 4, pp. 637-647. doi : 10.1142/S1793744211000485. http://archive.numdam.org/articles/10.1142/S1793744211000485/
[1] J. Aczél and Z. Dar´oczy, On Measures of Information and their Characterizations, Mathematics in Science and Engineering, Vol. 115 (Academic Press, 1975), xii+234 pp.
[2] D. Alspach and E. Odell, Lp spaces, in Handbook of the Geometry of Banach Spaces, Vol. I (North-Holland, 2001), pp. 123–159.
[3] G. Aubrun and I. Nechita, Catalytic majorization and lp norms, Comm. Math. Phys. 278(1) (2008) 133–144.
[4] G. Aubrun and I. Nechita, Stochastic domination for iterated convolutions and cat- alytic majorization, Ann. Inst. H. Poincaré Probab. Statist. 45 (2009) 611–625.
[5] R. Bhatia, Matrix Analysis, Graduate Texts in Mathematics, Vol. 169 (Springer- Verlag, 1997).
[6] F. Bohnenblust, An axiomatic characterization of Lp-spaces, Duke Math. J. 6 (1940) 627–640.
[7] H. Brézis, Analyse Fonctionnelle: Théorie et Applications (Masson, 1983) (in French).
[8] R. Cerf and P. Petit, A short proof of Cramér’s theorem, to appear in Amer. Math. Monthly (2011).
[9] C. Fern´andez-Gonz´alez, C. Palazuelos and D. Pérez-Garc´ıa, The natural rearrange- ment invariant structure on tensor products, J. Math. Anal. Appl. 343 (2008) 40–47.
[10] E. Howe, A new proof of Erd˝os’ theorem on monotone multiplicative functions, Amer. Math. Monthly 93 (1986) 593–595.
[11] J.-L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. (2) 104 (1976) 1–29.
[12] G. Kuperberg, The capacity of hybrid quantum memory, IEEE Trans. Inform. Th. 49 (2003) 1465–1473.
[13] T. Leinster, A multiplicative characterization of the power means, to appear in Bull. London Math. Soc. (2011).
[14] V. D. Milman and G. Schechtman, Asymptotic Theory of Finite-Dimensional Normed Spaces. With an Appendix by M. Gromov, Lecture Notes in Mathematics, Vol. 1200 (Springer-Verlag, 1986).
Cité par Sources :