Skip to main content
Log in

Putnam's theorem, Alexander's spectral area estimate, and VMO

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Alexander, H.: Projections of polynomial hulls. J. Funct. Anal.13, 13–19 (1973)

    Google Scholar 

  2. Alexander, H.: On the area of the spectrum of an element of a uniform algebra In: Complex approximation Proceedings, Quebec, July 3–8, 1978, pp. 3–12, ed. Aupetit, B.. Basel, Boston, Stuttgart: Birkhäuser 1980

    Google Scholar 

  3. Alexander, H., Taylor, B.A., Ullman, J.L.: Areas of projections of analytic sets. Invent. Math.16, 335–341 (1972)

    Google Scholar 

  4. Axler, S.: Subalgebras ofL . Ph. D. thesis. Berkeley: University of California 1975

    Google Scholar 

  5. Baernstein II, A.: Analytic functions of bounded mean oscilation. In: Aspects of content porary complex analysis. ed. Brannan, D.A., Clunie, J.G., pp. 3–36. London, New York: Academic Press 1980

    Google Scholar 

  6. Clancey, K.F., Gosselin, J.A.: On the local theory of Toeplitz operators. Ill. J. Math22, 449–458 (1978)

    Google Scholar 

  7. Coifman, R.R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. Math.103, 611–635 (1976)

    Google Scholar 

  8. Conway, J.B.: Subnormal operators. Res. Notes math., Vol. 51. San Francisco, London. Melbourne: Pitman 1981

    Google Scholar 

  9. Davie, A.M., Jewell, N.P.: Toeplitz operators in several complex variables. J. Funct. Anal.26, 356–368 (1977)

    Google Scholar 

  10. Dixmier, J.:C *-algebras. In: North-Holland Mathematical Library. Vol. 15. Amsterdam, New York, Oxford: North-Holland 1977

    Google Scholar 

  11. Douglas, R.G.: Banach algebra techniques in operator theory. Pure Appl. Math., vol 49 London, New York: Academic Press 1972

    Google Scholar 

  12. Douglas, R.G.: Banach algebra techniques in the theory of Toeplitz operators. CBMS Reg Conf. Ser. Math., No. 15. Philadelphia: Am. Math. Soc. 1973

    Google Scholar 

  13. Douglas, R.G.: Local Toeplitz operators. Proc. Lond. Math. Soc.36, 243–272 (1978)

    Google Scholar 

  14. Garnett, J.B.: Bounded analytic functions. London, New York: Academic Press 1981

    Google Scholar 

  15. Hansen, L.J.: The Hardy class of a function with slowly-growing area. Proc. Am. math. Soc.45, 409–410 (1974)

    Google Scholar 

  16. Hoffman, K.: Banach spaces of analytic functions. New York: Prentice Hall 1962

    Google Scholar 

  17. Krantz, S.G.: Holomorphic functions of bounded mean oscillation and mapping properties of the Szego projection. Duke Math. J.47, 743–761 (1980)

    Google Scholar 

  18. McDonald, G.: The maximal ideal space ofH +C on the ball in ℂn. Can. J. Math.31, 79–86 (1979)

    Google Scholar 

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

    Google Scholar 

  20. Rudin, W.: Function theory in the unit ball of ℂn. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  21. Sarason, D.: On products of Toeplitz operators. Acta Sci. Math.35, 7–12 (1973)

    Google Scholar 

  22. Sarason, D.: Functions of vanishing mean oscillation. Trans. Am. Math. Soc.207, 391–405 (1975)

    Google Scholar 

  23. Sarason, D.: Algebras betweenL , andH , spaces of analytic functions. Lect. Notes Math., Vol. 512, eds. Dold, A., Eckmann, B. pp. 117–129. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  24. Sarason, D.: Function theory on the unit circle. Virginia Polytechnic Institute and State University, 1978

  25. Schark, I.J.: Maximal ideals in an algebra of bounded analytic functions. J. Math. Mech.10, 735–746 (1961)

    Google Scholar 

  26. Stegenga, D.A.: A geometric condition which implies BMOA. In: Harmonic analysis in Euclidean spaces. Proc. Symp. Pure Math., Vol. 35, Part 1, pp. 427–430. Providence: Am. Math. Soc. 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Both authors were partially supported by the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Axler, S., Shapiro, J.H. Putnam's theorem, Alexander's spectral area estimate, and VMO. Math. Ann. 271, 161–183 (1985). https://doi.org/10.1007/BF01455985

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01455985

Keywords

Navigation