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Integral operators: Traces, index, and homology

Part of the Lecture Notes in Mathematics book series (LNM,volume 345)

Keywords

  • Bilinear Form
  • Toeplitz Operator
  • Essential Spectrum
  • Functional Calculus
  • Homology Class

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References

  1. M. Atiyah and I. M. Singer, Index of elliptic operators I, II, III, Annals of Math. 87 (1968).

    Google Scholar 

  2. I. D. Berg, An extension of the Weyl-Von Neumann Theorem to normal operators, Trans. A.M.S. 160 (1971) 365–371.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. L. Brown, R. G. Douglas, P. Fillmore, Unitary equivalence modulo the compact operators and extensions of C*-algebras, these Notes.

    Google Scholar 

  4. C. Berger and B. I. Show, Self-commutators of multi-cyclic hyponormal operators are always trace class, Bull. A.M.S. (See also their paper in these Notes.)

    Google Scholar 

  5. K. Clancy, Semi-normal operators with compact self-commutators, Proc. A.M.S. 26 (1970), 447–454.

    CrossRef  Google Scholar 

  6. K. Clancy, Examples of non-normal semi-normal operators whose spectra are non-spectral sets, Proc. A.M.S. 24 (1970) 497–800.

    Google Scholar 

  7. I. Colojoara, C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.

    MATH  Google Scholar 

  8. R. Carey, J. D. Pincus, The structure of intertwining isometries, Indiana Journal 22 (1973) 679–703.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. R. Carey, J. D. Pincus, On an invariant for certain operator algebras (to appear).

    Google Scholar 

  10. R. G. Douglas, Banach algebra techniques in the theory of Toeplitz operators, AMS Region Conf. Series in Math., 15 (1973).

    Google Scholar 

  11. Deddens and J. Stampfli, On a question of Douglas and Fillmore, Bull. A.M.S. 79 (1973).

    Google Scholar 

  12. N. Dunford and J. Schwartz, Linear operators I, Interscience, New York, 1967.

    MATH  Google Scholar 

  13. H. Federer, Geometric Measure Theory, Springer, 1969.

    Google Scholar 

  14. Gohberg and M. G. Krein, Introduction to the theory of linear non-self adjoint operators, Trans. Math. Monog. A.M.S. 18 (1969).

    Google Scholar 

  15. R. E. Howe, A functional calculus for hyponormal operators, to appear in Indiana Journal.

    Google Scholar 

  16. T. Kato, Smooth operators and commutators, Studia Math. 31 (1968) 535–546.

    MathSciNet  MATH  Google Scholar 

  17. C.R.F. Maunder, Algebraic Topology, Van Nostrand, New York, 1970.

    MATH  Google Scholar 

  18. B. McCoy and T. T. Woo, The two-dimensional Ising model, Harvard University Press.

    Google Scholar 

  19. J. D. Pincus, Commutators and systems of singular integral equations I, Acta Math. 121 (1968).

    Google Scholar 

  20. J. D. Pincus, The determining function method in the treatment of commutator systems, Proc. Intern. Conf. Operator Theory, Tihany (Hungary) (1970).

    Google Scholar 

  21. J. D. Pincus, On the trace of commutators in the algebra of operators generated by an algebra with trace class self-commutator (to appear).

    Google Scholar 

  22. J. D. Pincus, The spectrum of semi-normal operators, Proc. Nat. Ac. Sci. U.S.A. 68 (1971).

    Google Scholar 

  23. C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Zeitschrift, 116 (1970) 323–330.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. C. R. Putnam, Trace normal inequalities of the measure of hyponormal spectral, Indiana Journal 21 (1972).

    Google Scholar 

  25. C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Springer, New York, 1967.

    CrossRef  MATH  Google Scholar 

  26. M. Rosenbloom, A spectral theory for self-adjoint singular integral operators, Amer. J. Math. 88 (1966) 314–328.

    CrossRef  MathSciNet  Google Scholar 

  27. H. Royden, Real Analysis, McMillan, New York, 1964.

    MATH  Google Scholar 

  28. W. Rudin.

    Google Scholar 

  29. M. Venugopalkrishna, Fredholm operators associated with strongly pseudo-convex domains in Cn, J. Functional Analysis 9 (1972) 349–373.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. Xa-Dao-Xeng, On non-normal operators, Chinese Math. 3 (1963) 232–246.

    MathSciNet  Google Scholar 

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© 1973 Springer-Verlag

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Helton, J.W., Howe, R.E. (1973). Integral operators: Traces, index, and homology. In: Fillmore, P.A. (eds) Proceedings of a Conference on Operator Theory. Lecture Notes in Mathematics, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058919

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  • DOI: https://doi.org/10.1007/BFb0058919

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