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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Extensions of the index in factors of type $\textrm {II}_{\infty }$

Author: Michael Gartenberg
Journal: Proc. Amer. Math. Soc. 43 (1974), 163-168
MSC: Primary 46L10
MathSciNet review: 0328614
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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.

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Keywords: Index of a semi-Fredholm operator, von Neumann algebra, factor of type <!– MATH ${\Pi _\infty }$ –> <IMG WIDTH="38" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\Pi _\infty }$">
Article copyright: © Copyright 1974 American Mathematical Society