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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isomorphic $ \ell^p$-subspaces in Orlicz-Lorentz sequence spaces


Authors: Anna Kaminska and Yves Raynaud
Journal: Proc. Amer. Math. Soc. 134 (2006), 2317-2327
MSC (2000): Primary 46E30, 46B20, 46B45
Published electronically: February 3, 2006
MathSciNet review: 2213705
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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.


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Additional Information

Anna Kaminska
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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08266-9
PII: S 0002-9939(06)08266-9
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
Article copyright: © Copyright 2006 American Mathematical Society