Geodesic
Analytic Toeplitz and Composition Operators
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 859-865

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is a continuation of [1] where we began the study of intertwining analytic Toeplitz operators. Recall that X intertwines two operators A and B if XA = BX. Let H2 be the Hilbert space of analytic functions in the open unit disk D for which the functions fr(θ) = f(reiθ) are bounded in the L2 norm, and H∞ be the set of bounded functions in H2. For φ ∊ Hφ, Tφ (or Tφ(z)) is the analytic Toeplitz operator defined on H2 by the relation (T φf)(z) = φ(z)f(z). For φ ∊ H∞, we shall denote {φ(z): |z| < 1} by Range (φ) or φ(D). Then where and σ(Tφ) = Closure(φ(D)) [1]. If φ ∊ H∞ maps D into D, then we define the composition operator C φ on H2 by the relation (Cφ f) (z) = f(φ(z)). J. Ryff has shown [11, Theorem 1] that Cφ , is a bounded linear operator on H2. 
Deddens, James A. Analytic Toeplitz and Composition Operators. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 859-865. doi: 10.4153/CJM-1972-085-8
@article{10_4153_CJM_1972_085_8,
     author = {Deddens, James A.},
     title = {Analytic {Toeplitz} and {Composition} {Operators}},
     journal = {Canadian journal of mathematics},
     pages = {859--865},
     year = {1972},
     volume = {24},
     number = {5},
     doi = {10.4153/CJM-1972-085-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-085-8/}
}
TY  - JOUR
AU  - Deddens, James A.
TI  - Analytic Toeplitz and Composition Operators
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 859
EP  - 865
VL  - 24
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-085-8/
DO  - 10.4153/CJM-1972-085-8
ID  - 10_4153_CJM_1972_085_8
ER  - 
%0 Journal Article
%A Deddens, James A.
%T Analytic Toeplitz and Composition Operators
%J Canadian journal of mathematics
%D 1972
%P 859-865
%V 24
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-085-8/
%R 10.4153/CJM-1972-085-8
%F 10_4153_CJM_1972_085_8

[1] 1. Deddens, J. A., Intertwining analytic Toeplitz operators, Michigan Math. J. 18 (1971), 243–246. Google Scholar

[2] 2. Douglas, R. G., On majorization, factorization and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. Google Scholar

[3] 3. Duren, P. L., On the spectrum of a Toeplitz operator, Pacific J. Math. 14 (1964), 21–29. Google Scholar

[4] 4. Duren, P. L., Theory of Hp spaces (Academic Press, New York, 1970). Google Scholar

[5] 5. Halmos, P. R., A Hilbert space problem book (Van Nostrand, Princeton, 1967). Google Scholar

[6] 6. Hardy, G. H., Divergent series (Oxford University Press, Oxford, 1949). Google Scholar

[7] 7. Hoffman, K., Banach spaces of analytic functions (Prentice Hall, Englewood Cliffs, 1962). Google Scholar

[8] 8. Kriete, K. L. and David, Trutt, The Cesaro operator in I2 is subnormal, Amer. J. Math., 93 (1971), 215–225. Google Scholar

[9] 9. Lohwater, A. J. and Frank, Ryan, A distortion theorem for a class of conformal mappings, Mathematical essays dedicated to Maclntyre, A. J. (Ohio University Press, Athens, 1970). Google Scholar

[10] 10. Nordgren, E. A., Composition operators, Can. J. Math. 20 (1968), 442–449. Google Scholar

[11] 11. Ryff, J. V., Subordinate Hp functions, Duke Math. J., 33 (1966), 347–354. Google Scholar

[12] 12. Schwartz, H. J., Composition operators on Hp, Doctoral dissertation, University of Toledo, 1969. Google Scholar

[13] 13. Shields, A. L. and Wallen, L. J., The commutants of certain Hilbert space operators, Indiana J. Math. 20 (1971), 777–788. Google Scholar

[14] 14. Yoshino, T., Subnormal operator with a cyclic vector, Tôhoku Math. J. 21 (1969), 49–55. Google Scholar

Cité par Sources :