Embedding $l_{p}^{n^{\alpha }}$ in $l^{n}_{p,q}$
HTML articles powered by AMS MathViewer
- by N. L. Carothers and P. H. Flinn PDF
- Proc. Amer. Math. Soc. 88 (1983), 523-526 Request permission
Abstract:
It is shown that for $1 < p < \infty$, $1 \leqslant q \leqslant \infty$ and $0 < \alpha < 1$, there is a constant $C = C(p,q,\alpha ) < \infty$ such that $l_p^k$ is $C$-isomorphic to a subspace of $l_{p,q}^n$ where $k = O({n^\alpha })$.References
- G. D. Allen, Duals of Lorentz spaces, Pacific J. Math. 77 (1978), no.ย 2, 287โ291. MR 510924, DOI 10.2140/pjm.1978.77.287
- Z. Altshuler, The modulus of convexity of Lorentz and Orlicz sequence spaces, Notes in Banach spaces, Univ. Texas Press, Austin, Tex., 1980, pp.ย 359โ378. MR 606225 N. L. Carothers, Dissertation, Ohio State Univ., 1982. P. H. Flinn, Dissertation, Ohio State Univ., 1981. Y. Gordon and S. Reisner, Some geometric properties of Banach spaces of polynomials, preprint.
- Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249โ276. MR 223874
- W. B. Johnson, B. Maurey, G. Schechtman, and L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. 19 (1979), no.ย 217, v+298. MR 527010, DOI 10.1090/memo/0217
- J. L. Krivine, Sous-espaces de dimension finie des espaces de Banach rรฉticulรฉs, Ann. of Math. (2) 104 (1976), no.ย 1, 1โ29. MR 407568, DOI 10.2307/1971054
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 523-526
- MSC: Primary 46B15; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699425-9
- MathSciNet review: 699425