Isomorphisms of Cartesian Products of $\ell $-Power Series Spaces

E. Karapınar ¹   ; M. Yurdakul ²   ; V. Zahariuta ³

¹ Izmir University of Economics Izmir, Turkey
² Department of Mathematics Middle East Technical University 06531, Ankara, Turkey
³ FENS Sabancı University Istanbul, Turkey

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 2, pp. 103-111

Résumé

Let $\ell$ be a Banach sequence space with a monotone norm $\Vert \cdot \Vert_{\ell}$, in which the canonical system $(e_i)$ is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products $E^{\ell}_0(a)\times E^{\ell}_{\infty}(b) $ where $E^{\ell}_0(a) = K^{\ell}(\exp (-{p}^{-1} a_i))$ and $E^{\ell}_{\infty}(b) = K^{\ell}(\exp ({p} a_i))$ are finite and infinite $\ell$-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.

Détail

DOI : 10.4064/ba54-2-2

Keywords: ell banach sequence space monotone norm vert cdot vert ell which canonical system normalized symmetric basis complete isomorphic classification cartesian products ell times ell infty where ell ell exp ell infty ell exp finite infinite ell power series spaces respectively classification generalization results chalov studia math djakov michigan math using method compound linear topological invariants developed third author