Geodesic
Toeplitz operators on abstract Hardy spaces
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 129-131

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

In [10], C. Sundberg uses a clever argument involving an idea of Davie and Jewell [13] to prove an isomorphism theorem for a very general class of operators. A related spectral inclusion theorem is an immediate consequence of the proof of this result, as Sundberg points out. He goes on to list several well known examples that are applications of his main result and remarks that the proof of the McDonald–Sundberg theorem (c.f. [9]) can now be considerably simplified. The purpose of this note is to give further evidence of the utility of the criterion established in [10]. Here and throughout X denotes a compact Hausdorff space and A is a function algebra on X. The Shilovboundary of A is the minimal closed subset ∂(A) of X with the property that. 
Smith, R. C. Toeplitz operators on abstract Hardy spaces. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 129-131. doi: 10.1017/S0017089500007138
@article{10_1017_S0017089500007138,
     author = {Smith, R. C.},
     title = {Toeplitz operators on abstract {Hardy} spaces},
     journal = {Glasgow mathematical journal},
     pages = {129--131},
     year = {1988},
     volume = {30},
     number = {2},
     doi = {10.1017/S0017089500007138},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007138/}
}
TY  - JOUR
AU  - Smith, R. C.
TI  - Toeplitz operators on abstract Hardy spaces
JO  - Glasgow mathematical journal
PY  - 1988
SP  - 129
EP  - 131
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007138/
DO  - 10.1017/S0017089500007138
ID  - 10_1017_S0017089500007138
ER  - 
%0 Journal Article
%A Smith, R. C.
%T Toeplitz operators on abstract Hardy spaces
%J Glasgow mathematical journal
%D 1988
%P 129-131
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007138/
%R 10.1017/S0017089500007138
%F 10_1017_S0017089500007138

[1] 1.Abrahamse, M. B., Toeplitz operators in multiply connected domains, Amer. J. Math. 96 (1974), 261–297. Google Scholar | DOI

[2] 2.Axler, S., Conway, J. B. and McDonald, G., Toeplitz operators on Bergman spaces, Canad. J. Math. 34 (1982), 466–483. Google Scholar | DOI

[3] 3.Davie, A. M. and Jewell, N. P., Toeplitz operators in several complex variables, J. Functional Analysis 26 (1977), 356–368. Google Scholar | DOI

[4] 4.Douglas, R. G., Banach algebra techniques in operator theory (Academic Press, 1972). Google Scholar

[5] 5.Gamelin, T. W., Uniform algebras (Prentice Hall, Englewood Cliffs, New Jersey, 1969). Google Scholar

[6] 6.Gamelin, T. W., Rational approximation theory (UCLA Course Notes, 1975). Google Scholar

[7] 7.Janas, J., Toeplitz operators for a certain class of function algebras, Studia Math. 55 (1976), 157–161. Google Scholar | DOI

[8] 8.Janas, J., Toeplitz operators for hypo-Dirichlet algebras, Ann. Polon. Math. 37 (1980), 249–254. Google Scholar | DOI

[9] 9.McDonald, G. and Sundberg, C., Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595–611. Google Scholar | DOI

[10] 10.Sundberg, C., Exact sequences for generalized Toeplitz operators, preprint. Google Scholar

Cité par Sources :