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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 $ {\rm II}\sb{\infty }$


Author: Michael Gartenberg
Journal: Proc. Amer. Math. Soc. 43 (1974), 163-168
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1974-0328614-2
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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DOI: https://doi.org/10.1090/S0002-9939-1974-0328614-2
Keywords: Index of a semi-Fredholm operator, von Neumann algebra, factor of type $ {\Pi _\infty }$
Article copyright: © Copyright 1974 American Mathematical Society