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

Volume 204 / 2011

Peter Chalov, Vyacheslav Zakharyuta Studia Mathematica 204 (2011), 275-282 MSC: Primary 46A32; Secondary 46A04. DOI: 10.4064/sm204-3-6


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].


  • Peter ChalovDepartment of Mathematics
    South Federal University
    344090 Rostov-na-Donu, Russia
  • Vyacheslav ZakharyutaSabanci University
    34956 Istanbul, Turkey

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