Isomorphic $\ell ^p$-subspaces in Orlicz-Lorentz sequence spaces
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- by Anna Kamińska and Yves Raynaud PDF
- Proc. Amer. Math. Soc. 134 (2006), 2317-2327 Request permission
Abstract:
Given a decreasing weight $w$ and an Orlicz function $\varphi$ satisfying the $\Delta _2$-condition at zero, we show that the Orlicz-Lorentz sequence space $d(w,\varphi )$ contains an $(1+\epsilon )$-isomorphic copy of $\ell _p, 1\le p<\infty$, if and only if the Orlicz sequence space $\ell _\varphi$ does, that is, if $p\in [\alpha _\varphi , \beta _\varphi ]$, where $\alpha _\varphi$ and $\beta _\varphi$ are the Matuszewska-Orlicz lower and upper indices of $\varphi$, respectively. If $\varphi$ does not satisfy the $\Delta _2$-condition, then a similar result holds true for order continuous subspaces $d_0(w,\varphi )$ and $h_\varphi$ of $d(w,\varphi )$ and $\ell _\varphi$, respectively.References
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Additional Information
- Anna Kamińska
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- Email: kaminska@memphis.edu
- Yves Raynaud
- Affiliation: Institut de Mathématiques de Jussieu, (case 186) CNRS & Université Paris-6, 4, place Jussieu, 75252 Paris cedex 05, France
- Email: yr@ccr.jussieu.fr
- Received by editor(s): December 7, 2004
- Received by editor(s) in revised form: March 6, 2005
- Published electronically: February 3, 2006
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2317-2327
- MSC (2000): Primary 46E30, 46B20, 46B45
- DOI: https://doi.org/10.1090/S0002-9939-06-08266-9
- MathSciNet review: 2213705