Proceedings of the American Mathematical Society

Author(s): Anna Kaminska; Yves Raynaud
Journal: Proc. Amer. Math. Soc. 134 (2006), 2317-2327.
MSC (2000): Primary 46E30, 46B20, 46B45
Posted: February 3, 2006
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Abstract: Given a decreasing weight

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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Anna Kaminska
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Email: kaminska@memphis.edu

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