Isomorphisms of Cartesian Products of $\ell $-Power Series Spaces
Volume 54 / 2006
Bulletin Polish Acad. Sci. Math. 54 (2006), 103-111
MSC: Primary 46A45.
DOI: 10.4064/ba54-2-2
Abstract
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.
