On operators from $ℓ_{s}$ to $ℓ_{p} ⊗̂ ℓ_{q}$ or to $ℓ_{p} \widehat{⊗̂} ℓ_{q}$

Christian Samuel

On operators from

ℓ_{s}

ℓ_{p} \otimes ̂ ℓ_{q}

or to

ℓ_{p} \hat{\otimes ̂} ℓ_{q}

Christian Samuel

Colloquium Mathematicae, Tome 120 (2010), p. 25-33 / Harvested from The Polish Digital Mathematics Library

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Résumé

We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:283586

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     author = {Christian Samuel},
     title = {On operators from $l\_{s}$ to $l\_{p} [?] l\_{q}$ or to $l\_{p} \widehat{[?]} l\_{q}$
            },
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {25-33},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-1-3}
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Christian Samuel. On operators from $ℓ_{s}$ to $ℓ_{p} ⊗̂ ℓ_{q}$ or to $ℓ_{p} \widehat{⊗̂} ℓ_{q}$
            . Colloquium Mathematicae, Tome 120 (2010) pp. 25-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-1-3/