Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

E. Karapınar; M. Yurdakul; V. Zahariuta

E. Karapınar ; M. Yurdakul ; V. Zahariuta

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006), p. 103-111 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let ℓ be a Banach sequence space with a monotone norm $∥ \cdot ∥_{ℓ}$ , in which the canonical system $(e_{i})$ is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products $E_{0}^{ℓ} (a) \times E_{\infty}^{ℓ} (b)$ where $E_{0}^{ℓ} (a) = K^{ℓ} (e x p (- p^{- 1} a_{i}))$ and $E_{\infty}^{ℓ} (b) = K^{ℓ} (e x p (p a_{i}))$ are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by the third author.

Publié le : 2006-01-01

Zbl 1116.46005

EUDML-ID : urn:eudml:doc:280915

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     title = {Isomorphisms of Cartesian Products of l-Power Series Spaces},
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     pages = {103-111},
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E. Karapınar; M. Yurdakul; V. Zahariuta. Isomorphisms of Cartesian Products of ℓ-Power Series Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) pp. 103-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-2/