A factorization constant for $l^ n_ p$, $0<p<1$
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- by N. T. Peck PDF
- Proc. Amer. Math. Soc. 121 (1994), 423-427 Request permission
Abstract:
We prove that if PT is a factorization of the identity operator on $\ell _p^n$ through $\ell _\infty ^k,0 < p$, then $\left \| P \right \| \left \| T \right \| \geq C{n^{1/p - 1/2}}{(\log n)^{ - 1/2}}$. This is a corollary of a more general result on factoring the identity operator on a quasi-normed space X through $\ell _\infty ^k$.References
- J. Bourgain, J. Lindenstrauss, and V. Milman, Approximation of zonoids by zonotopes, Acta Math. 162 (1989), no.ย 1-2, 73โ141. MR 981200, DOI 10.1007/BF02392835
- N. J. Kalton, The three space problem for locally bounded $F$-spaces, Compositio Math. 37 (1978), no.ย 3, 243โ276. MR 511744
- Gideon Schechtman, More on embedding subspaces of $L_p$ in $l^n_r$, Compositio Math. 61 (1987), no.ย 2, 159โ169. MR 882972
- Michel Talagrand, Embedding subspaces of $L_1$ into $l^N_1$, Proc. Amer. Math. Soc. 108 (1990), no.ย 2, 363โ369. MR 994792, DOI 10.1090/S0002-9939-1990-0994792-4
- Nicole Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 993774
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 423-427
- MSC: Primary 46A16; Secondary 46B07
- DOI: https://doi.org/10.1090/S0002-9939-1994-1233980-2
- MathSciNet review: 1233980