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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The finite fibre problem and an index formula for elementary operators


Authors: Jörg Eschmeier and Mihai Putinar
Journal: Proc. Amer. Math. Soc. 123 (1995), 743-746
MSC: Primary 47A13; Secondary 47A53, 47B47
MathSciNet review: 1219725
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Abstract: Let $ J \subset L(K,H)$ be an operator ideal between Hilbert spaces, and let $ S \in L{(H)^n},T \in L{(K)^n}$ be commuting tuples of continuous linear operators. It is shown that the elementary operator $ R:J \to J,A \to \sum\nolimits_{i = 1}^n {{S_i}A{T_i}} $ determined by S and T satisfies the finite fibre property. As a consequence it follows that an index formula proved by L. Fialkow for elementary operators under the additional assumption of the finite fibre property holds true in general.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1219725-1
PII: S 0002-9939(1995)1219725-1
Article copyright: © Copyright 1995 American Mathematical Society