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


Index of Fredholm operators

Author: Kung Wei Yang
Journal: Proc. Amer. Math. Soc. 41 (1973), 329-330
MSC: Primary 47B30
MathSciNet review: 0318946
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Abstract: Let $ X,Y,Z$ be Banach spaces, and let $ T:X \to Y$ and $ S:Y \to Z$ be Fredholm operators. Let $ \operatorname{ind} (T)$ denote the index of $ T$. A short proof is given for the identity $ \operatorname{ind} (ST) = \operatorname{ind} (S) + \operatorname{ind} (T)$.

References [Enhancements On Off] (What's this?)

  • [1] Hyman Bass, Algebraic 𝐾-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491 (40 #2736)
  • [2] J. Dieudonné, Foundations of modern analysis, Academic Press, New York-London, 1969. Enlarged and corrected printing; Pure and Applied Mathematics, Vol. 10-I. MR 0349288 (50 #1782)
  • [3] Richard S. Palais, Seminar on the Atiyah-Singer index theorem, With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. MR 0198494 (33 #6649)

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Additional Information

PII: S 0002-9939(1973)0318946-5
Keywords: Index of Fredholm operator
Article copyright: © Copyright 1973 American Mathematical Society