Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T19:23:56.571Z Has data issue: false hasContentIssue false
  • English
  • Français

Inner Functions and Toeplitz Operators

Published online by Cambridge University Press:  20 November 2018

Gerard J. Murphy
Gerard J. Murphy*
Affiliation:
Department of Mathematics University College Cork Ireland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give characterizations of Toeplitz operators on generalised H2 spaces and derive some properties of the corresponding Toeplitz algebras. The proofs depend essentially on having a "sufficient" supply of inner functions.

Keywords

47B3547C1546J15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 324 - 331
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Axler, S., Bergman spaces and their operators. In: Surveys of some Recent Results in Operator Theory, Vol. I, (eds. Conway, J. B. and B. B. Morrel), Pitman Res. Notes in Math. 171, Longman, Essex-New York, 1988.Google Scholar
2. Bernard, A., Garnett, J. B. and Marshall, D. E., Algebras generated by inner functions, J. Funct. Anal. 25(1977), 275–285.Google Scholar
3. Boutet, L. de Monvel, On the index of Toeplitz operators of several complex variables, Invent. Math. 50(1979), 249–272.Google Scholar
4. Browder, A., Introduction to Function Algebras, Benjamin, New York-Amsterdam, 1969.Google Scholar
5. Coburn, L. A., Douglas, R. G., Schaeffer, D. and Singer, I. M., C*-algebras of operators on a half-space II, Index theory, Inst. Hautes Etudes Sci. Publ. Math. 40(1971), 69–79.Google Scholar
6. Devinatz, A., Toeplitz operators on H1-spaces, Trans. Amer. Math. Soc. 112(1964), 304–317.Google Scholar
7. Leibowitz, G., Lectures on Complex Function Algebras, Scott-Foresman, Illinois, 1970.Google Scholar
8. Muhly, P. and Renault, J., C* -algebras of multivariate Wiener-Hopf operators, Trans. Amer. Math. Soc. 274(1982), 1–44.Google Scholar
9. Murphy, G. J., Ordered groups and Toeplitz C*-algebras, J. Operator Theory 18(1987), 303–326.Google Scholar
10. Murphy, G. J., Spectral and index theory for Toeplitz operators, Proc. Royal Irish Acad. (A) 91(1991), 1–6.Google Scholar
11. Murphy, G. J., Almost-invertible Toeplitz operators and K-theory, Integral Equations and Operator Theory 15 (1992), 72–81.Google Scholar
12. Murphy, G. J., An index theorem for Toeplitz operators, J. Operator Theory, to appear.Google Scholar
13. Murphy, G. J., Toeplitz operators on generalised H2 spaces, Integral Equations and Operator Theory 15(1992), 825–852.Google Scholar
14. Tomiyama, J. and Yabuta, K., Toeplitz operators for uniform algebras, Tôhoko Math. J. 30(1978), 117–129.Google Scholar
15. Upmeier, H., Fredholm indices for Toeplitz operators on bounded symmetric domains, Amer. J. Math. 110(1988), 811–832.Google Scholar
16. Upmeier, H., Toeplitz operators on bounded symmetric domains, Trans. Amer. Math. Soc. 280(1983), 221–237.Google Scholar