Unicellularity of the multiplication operator on Banach spaces of formal power series

B. Yousefi

B. Yousefi

Studia Mathematica, Tome 147 (2001), p. 201-209 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ${β (n)}_{n = 0}^{\infty}$ be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space $ℓ^{p} (β)$ of all power series $f (z) = \sum_{n = 0}^{\infty} f ̂ (n) z ⁿ$ such that $\sum_{n = 0}^{\infty} {| f ̂ (n) |}^{p} {| β (n) |}^{p} < \infty$ . We give some sufficient conditions for the multiplication operator, $M_{z}$ , to be unicellular on the Banach space $ℓ^{p} (β)$ . This generalizes the main results obtained by Lu Fang [1].

Publié le : 2001-01-01

Zbl 0995.47020

EUDML-ID : urn:eudml:doc:286211

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     title = {Unicellularity of the multiplication operator on Banach spaces of formal power series},
     journal = {Studia Mathematica},
     volume = {147},
     year = {2001},
     pages = {201-209},
     zbl = {0995.47020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-1}
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B. Yousefi. Unicellularity of the multiplication operator on Banach spaces of formal power series. Studia Mathematica, Tome 147 (2001) pp. 201-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-1/