Extensions of the index in factors of type 𝐼𝐼_{∞}

Gartenberg, Michael

doi:10.1090/S0002-9939-1974-0328614-2

Extensions of the index in factors of type $\textrm {II}_{\infty }$
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Proc. Amer. Math. Soc. 43 (1974), 163-168 Request permission

Abstract:

In this paper we show that the analytic index has no continuous extension to those operators in a factor of type ${\Pi _\infty }$ on a separable Hilbert space which are not semi-Fredholm in the Breuer sense. A similar result has already been proved by Coburn and Lebow [3] for factors of type ${I_\infty }$. Here we use Breuer’s generalized Fredholm theory to extend their result to the more general setting.

References

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