Isomorphic classification of the tensor products $ E_{0}( \exp \alpha i)\mathbin{ \widehat{\otimes }}E_{\infty }( \exp\beta j) $

Peter Chalov¹ ; Vyacheslav Zakharyuta²

¹Department of Mathematics South Federal University 344090 Rostov-na-Donu, Russia
²Sabanci University 34956 Istanbul, Turkey

Studia Mathematica, Tome 204 (2011) no. 3, pp. 275-282

Résumé

It is proved, using so-called multirectangular invariants, that the condition $\alpha \beta =\tilde{\alpha}\tilde{\beta}$ is sufficient for the isomorphism of the spaces $E_{0}(\exp \alpha i)\mathbin{\widehat{\otimes}}E_{\infty }(\exp \beta j)$ and $E_{0}(\exp \tilde{\alpha}i)\mathbin{\widehat{\otimes}}E_{\infty }(\exp \tilde{\beta}j)$. This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].

Détail

DOI : 10.4064/sm204-3-6

Keywords: proved using so called multirectangular invariants condition alpha beta tilde alpha tilde beta sufficient isomorphism spaces exp alpha mathbin widehat otimes infty exp beta exp tilde alpha mathbin widehat otimes infty exp tilde beta solves problem posed notice necessity has proved earlier