Copies of $l^1$ and $c_o$ in Musielak-Orlicz sequence spaces
Alherk, Ghassan ; Hudzik, Henryk
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 9-19 / Harvested from Czech Digital Mathematics Library
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Criteria in order that a Musielak-Orlicz sequence space $l^\Phi$ contains an isomorphic as well as an isomorphically isometric copy of $l^1$ are given. Moreover, it is proved that if $\Phi = (\Phi_i)$, where $\Phi_i$ are defined on a Banach space, $X$ does not satisfy the $\delta^o_2$-condition, then the Musielak-Orlicz sequence space $l^\Phi (X)$ of $X$-valued sequences contains an almost isometric copy of $c_o$. In the case of $X = I\!\!R$ it is proved also that if $l^\Phi$ contains an isomorphic copy of $c_o$, then $\Phi$ does not satisfy the $\delta^o_2$-condition. These results extend some results of [A] and [H2] to Musielak-Orlicz sequence spaces.

Publié le : 1994-01-01
Classification:  46B20,  46B25,  46B45,  46E30 
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     author = {Ghassan Alherk and Henryk Hudzik},
     title = {Copies of $l^1$ and $c\_o$ in Musielak-Orlicz sequence spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {9-19},
     zbl = {0820.46013},
     mrnumber = {1292578},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118636}
}

Alherk, Ghassan; Hudzik, Henryk. Copies of $l^1$ and $c_o$ in Musielak-Orlicz sequence spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 9-19. http://gdmltest.u-ga.fr/item/118636/

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