Mathematische Annalen

, Volume 271, Issue 2, pp 161–183

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

  • Sheldon Axler
  • Joel H. Shapiro


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  1. 1.
    Alexander, H.: Projections of polynomial hulls. J. Funct. Anal.13, 13–19 (1973)Google Scholar
  2. 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 1980Google Scholar
  3. 3.
    Alexander, H., Taylor, B.A., Ullman, J.L.: Areas of projections of analytic sets. Invent. Math.16, 335–341 (1972)Google Scholar
  4. 4.
    Axler, S.: Subalgebras ofL . Ph. D. thesis. Berkeley: University of California 1975Google Scholar
  5. 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 1980Google Scholar
  6. 6.
    Clancey, K.F., Gosselin, J.A.: On the local theory of Toeplitz operators. Ill. J. Math22, 449–458 (1978)Google Scholar
  7. 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. 8.
    Conway, J.B.: Subnormal operators. Res. Notes math., Vol. 51. San Francisco, London. Melbourne: Pitman 1981Google Scholar
  9. 9.
    Davie, A.M., Jewell, N.P.: Toeplitz operators in several complex variables. J. Funct. Anal.26, 356–368 (1977)Google Scholar
  10. 10.
    Dixmier, J.:C *-algebras. In: North-Holland Mathematical Library. Vol. 15. Amsterdam, New York, Oxford: North-Holland 1977Google Scholar
  11. 11.
    Douglas, R.G.: Banach algebra techniques in operator theory. Pure Appl. Math., vol 49 London, New York: Academic Press 1972Google Scholar
  12. 12.
    Douglas, R.G.: Banach algebra techniques in the theory of Toeplitz operators. CBMS Reg Conf. Ser. Math., No. 15. Philadelphia: Am. Math. Soc. 1973Google Scholar
  13. 13.
    Douglas, R.G.: Local Toeplitz operators. Proc. Lond. Math. Soc.36, 243–272 (1978)Google Scholar
  14. 14.
    Garnett, J.B.: Bounded analytic functions. London, New York: Academic Press 1981Google Scholar
  15. 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. 16.
    Hoffman, K.: Banach spaces of analytic functions. New York: Prentice Hall 1962Google Scholar
  17. 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. 18.
    McDonald, G.: The maximal ideal space ofH +C on the ball in ℂn. Can. J. Math.31, 79–86 (1979)Google Scholar
  19. 19.
    Putnam, C.R.: An inequality for the area of hyponormal spectra. Math. Z.116, 323–330 (1970)Google Scholar
  20. 20.
    Rudin, W.: Function theory in the unit ball of ℂn. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  21. 21.
    Sarason, D.: On products of Toeplitz operators. Acta Sci. Math.35, 7–12 (1973)Google Scholar
  22. 22.
    Sarason, D.: Functions of vanishing mean oscillation. Trans. Am. Math. Soc.207, 391–405 (1975)Google Scholar
  23. 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 1976Google Scholar
  24. 24.
    Sarason, D.: Function theory on the unit circle. Virginia Polytechnic Institute and State University, 1978Google Scholar
  25. 25.
    Schark, I.J.: Maximal ideals in an algebra of bounded analytic functions. J. Math. Mech.10, 735–746 (1961)Google Scholar
  26. 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. 1979Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Sheldon Axler
    • 1
  • Joel H. Shapiro
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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