Skip to main content

Composition operators on hilbert spaces

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 693))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. B. Abrahamse and J. A. Ball, Analytic Toeplitz operators with automorphic symbol II, to appear.

    Google Scholar 

  2. J. A. Ball, Hardy space expectation operators and reducing subspaces, Proc. Amer. Math. Soc. 47 (1975), 351–357. MR 50 #10887.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. R. Baxter, A class of ergodic transformations having simple spectrum, Proc. Amer. Math. Soc. 27 (1971), 275–279. MR 43 #2187.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. M. Belley, Spectral properties for invertible measuring preserving transformations, Canad. J. Math. 25 (1973), 806–811.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. M. Boyd, Composition operators on the Bergman space and analytic function spaces on the annulus, Thesis, U. North Carolina, 1974.

    Google Scholar 

  6. D. M. Boyd, Composition operators on the Bergman space, Coll. Math. 34 (1975), 127–136. MR 53 #11416.

    MathSciNet  MATH  Google Scholar 

  7. D. M. Boyd, Composition operators on H p(A), Pacific J. Math. 62 (1976), 55–60.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. G. Caughran, Polynomial approximation and spectral properties of composition operators on H 2, Indiana U. Math. J. 21 (1971), 81–84. MR 44 #4213.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. G. Caughran and H. J. Schwartz, Spectra of compact composition operators, Proc. Amer. Math. Soc. 51 (1975), 127–130. MR 51 #13750.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. R. Choksi, Nonergodic transformations with discrete spectrum, Illinois J. Math. 9 (1965), 307–320. MR 30 #4093.

    MathSciNet  MATH  Google Scholar 

  11. J. R. Choksi, Unitary operators induced by measure preserving transformations, J. Math. Mech. 16 (1966), 83–100. MR 34 #1844.

    MathSciNet  MATH  Google Scholar 

  12. J. R. Choksi, Unitary operators induced by measurable transformations, J. Math. Mech. 17 (1967/68), 785–801. MR 36 #2003.

    MathSciNet  MATH  Google Scholar 

  13. J. A. Cima, J. Thomson and W. Wogen, On some properties of composition operators, Indiana U. Math. J. 24 (1974), 215–220. MR 50 #2979.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. A. Cima and W. Wogen, On algebras generated by composition operators, Canad. J. Math. 26 (1974), 1234–1241. MR 50 #2978.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. A. Deddens, Analytic Toeplitz and composition operators, Canad. J. Math. 24 (1972), 859–865. MR 46 #9789.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. A. Denjoy, Sur l'iteration des fonctions analytiques, C. R. Acad. Sci. Paris 182 (1926), 255–257.

    MATH  Google Scholar 

  17. P. L. Duren, Theory of Hp Spaces, Academic Press, New York, 1970. MR 42 #3552.

    MATH  Google Scholar 

  18. L. Ford, Automorphic Functions, 2nd ed., Chelsea, N.Y. 1951.

    Google Scholar 

  19. P. R. Halmos, Measurable transformations, Bull. Amer. Math. Soc. 55 (1949), 1015–1034. MR 11-373.

    Article  MathSciNet  MATH  Google Scholar 

  20. P. R. Halmos, Measure Theory, Van Nostrand, Princeton, N.J., 1950. MR 11-504.

    Book  MATH  Google Scholar 

  21. P. R. Halmos, Lectures on Ergodic Theory, Chelsea, N.Y., 1956. MR 20 #3958.

    Google Scholar 

  22. P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, N.J., 1967. MR 34 #8178.

    MATH  Google Scholar 

  23. P. R. Halmos and J. von Neumann, Operator methods in classical mechanics, Ann. Math. 43 (1942), 332–350. MR 4–14.

    Article  MathSciNet  MATH  Google Scholar 

  24. F. Hartman, Inclusion theorems for Sonnenschein matrices, Proc. Amer. Math. Soc. 21 (1969), 513–519. MR 39 #5984.

    Article  MathSciNet  MATH  Google Scholar 

  25. A. Iwanik, Pointwise induced operators on Lp-spaces, Proc. Amer. Math. Soc. 58 (1976), 173–178.

    MathSciNet  MATH  Google Scholar 

  26. H. Kamowitz, The spectra of endomorphisms of the disc algebra, Pacific J. Math. 46 (1973), 433–440. MR 49 #5918.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Kamowitz, The spectra of composition operators on HP, J. Functional Anal. 18 (1975), 132–150. MR 53 #11417.

    Article  MathSciNet  MATH  Google Scholar 

  28. H. Kamowitz and S. Scheinberg, The spectrum of automorphisms of Banach algebras, J. Functional Anal. 4 (1969), 268–276. MR 40 #3316.

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Karlin and J. McGregor, Spectral theory of branching processes, Z. Wahrscheinlichkeitstheorie 5 (1966), 6–33. MR 34 #5167.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. L. Kelley, Weighted shifts on Hilbert space, Thesis, U. Michigan, 1966.

    Google Scholar 

  31. M. Koenig, Recherches sur les integrals de certains equations fonctionelles, Annales de l'Ecole Normale 3 (1884), 1–112.

    Google Scholar 

  32. B. O. Koopman, Hamiltonian systems and transformations in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 17 (1931), 315–318.

    Article  MATH  Google Scholar 

  33. B. O. Koopman and J. von Neumann, Dynamical systems of continuous spectra, Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 255–263.

    Article  MATH  Google Scholar 

  34. K. Kuratowski, Topology, Vol. 1, Academic Press, N.Y., 1966. MR 36 #840.

    MATH  Google Scholar 

  35. J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. 23 (1925), 481–519.

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Lubin, Isometries induced by composition operators and invariant subspaces, Illinois J. Math. 19 (1975), 424–427.

    MathSciNet  MATH  Google Scholar 

  37. J. von Neumann, Einige Satze über messbare Abbildungen, Ann. Math. (2) 33 (1932), 574–586.

    Article  MATH  Google Scholar 

  38. J. von Neumann, Zur operatoren methode in der klassischen Mechanik, Ann. Math. (2) 33(1932), 587–642, 789–791.

    Article  MATH  Google Scholar 

  39. E. A. Nordgren, Composition operators, Canad. J. Math. 20 (1968), 442–449. MR 36 #6961.

    Article  MathSciNet  MATH  Google Scholar 

  40. W. C. Ridge, Composition operators, Thesis, Indiana U., 1969.

    Google Scholar 

  41. W. C. Ridge, Spectrum of a composition operator, Proc. Amer. Math. Soc. 37 (1973), 121–127. MR 46 #5583.

    Article  MathSciNet  MATH  Google Scholar 

  42. W. C. Ridge, Characterization of abstract composition operators, Proc. Amer. Math. Soc. 45 (1974), 393–396. MR 49 #11310.

    Article  MathSciNet  MATH  Google Scholar 

  43. R. C. Roan, Composition operators on the space of functions with H p derivative, to appear.

    Google Scholar 

  44. R. C. Roan, Composition operators on a space of Lipschitz functions, to appear.

    Google Scholar 

  45. R. C. Roan, Composition operators on H p with dense range, Indiana U. Math. J., to appear.

    Google Scholar 

  46. W. Rudin, Analytic functions of class H p, Lectures on Functions of a Complex Variable (W. Kaplan ed.), U. Michigan Press,Ann Arbor, 1955. MR 17–24.

    Google Scholar 

  47. W. Rudin, Analytic functions of class Hp, Trans. Amer. Math. Soc. 78 (1955), 46–66. MR 16–810.

    MathSciNet  MATH  Google Scholar 

  48. J. V. Ryff, Subordinate H p functions, Duke Math. J. 33 (1966), 347–354. MR 33 #289.

    Article  MathSciNet  MATH  Google Scholar 

  49. D. E. Sarason, Weak-star generators of H , Pacific J. Math. 17 (1966), 519–528. MR 35 #2151.

    Article  MathSciNet  MATH  Google Scholar 

  50. H. J. Schwartz, Composition operators on Hp, Thesis, U. Toledo, 1969.

    Google Scholar 

  51. J. H. Shapiro and P. D. Taylor, Compact, nuclear, and Hilbert-Schmidt composition operators on H 2, Indiana U. Math. J. 23 (1973/74), 471–496. Mr 48 #4816.

    Article  MathSciNet  MATH  Google Scholar 

  52. A. L. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Mathematical Surveys, No. 13, Amer. Math. Soc., Providence, 1974. MR 50 #14341.

    MATH  Google Scholar 

  53. A. L. Shields and L. J. Wallen, The commutants of certain Hilbert space operators, Indiana U. Math. J. 20 (1971), 777–788. MR 44 #4558.

    Article  MathSciNet  MATH  Google Scholar 

  54. R. Sikorski, On the inducing of homomorphisms by mappings, Fund. Math. 36 (1949), 7–22. MR 11–166.

    MathSciNet  MATH  Google Scholar 

  55. R. Sikorski, Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Band 25, Springer-Verlag, Berlin, 1964. MR 31 #2178.

    Google Scholar 

  56. R. K. Singh, Composition operators, Thesis, U. New Hampshire, 1972.

    Google Scholar 

  57. R. K. Singh, Compact and quasinormal composition operators, Proc. Amer. Math. Soc. 45 (1974), 80–82. MR 50 #1043.

    Article  MathSciNet  MATH  Google Scholar 

  58. R. K. Singh, Normal and Hermitian composition operators, Proc. Amer. Math. Soc. 47 (1975), 348–350. MR 50 #8153.

    Article  MathSciNet  MATH  Google Scholar 

  59. R. K. Singh, Invertible composition operators on L2(λ), Proc. Amer. Math. Soc. 56 (1976), 127–129. MR 53 #3776.

    MathSciNet  Google Scholar 

  60. R. K. Singh, Composition operators induced by rational functions, Proc. Amer. Math. Soc. 59 (1976), 329–333. MR 54 #5895.

    Article  MathSciNet  MATH  Google Scholar 

  61. D. W. Swanton, Composition operators on Hp(D), Thesis, Northwestern U., 1974.

    Google Scholar 

  62. B. Sz.-Nagy, Über die Gesamtheit der charakteristischen Funktionen im Hilbertschen Funktionenraum, Acta Sci. Math. 9 (1937), 166–176.

    MATH  Google Scholar 

  63. G. Targonski, Seminar on functional operators and equations, Springer Lecture Notes #33, Springer-Verlag, Berlin, 1967. MR 36 #744.

    Book  MATH  Google Scholar 

  64. G. Targonski, Linear endomorphisms of function algebras and related functional equations, Indiana U. Math. J. 20 (1970), 579–589. MR 42 #5054.

    Article  MathSciNet  MATH  Google Scholar 

  65. J. Wolff, Sur l'iteration des fonctions, C. R. Acad. Sci. Paris 182 (1926), 42–43, 200–201.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

John M. Bachar Jr. Donald W. Hadwin

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Nordgren, E.A. (1978). Composition operators on hilbert spaces. In: Bachar, J.M., Hadwin, D.W. (eds) Hilbert Space Operators. Lecture Notes in Mathematics, vol 693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064659

Download citation

  • DOI: https://doi.org/10.1007/BFb0064659

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09097-7

  • Online ISBN: 978-3-540-35557-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics