Invertible Elements in the Dirichlet Space
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 419-422

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

It is shown that if a function in the Dirichlet space is inveritible then it is cyclic with respect to the operator of multiplication by the identity function.
DOI : 10.4153/CMB-1990-068-7
Mots-clés : 30H05, 46E20, 47B37
Brown, Leon. Invertible Elements in the Dirichlet Space. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 419-422. doi: 10.4153/CMB-1990-068-7
@article{10_4153_CMB_1990_068_7,
     author = {Brown, Leon},
     title = {Invertible {Elements} in the {Dirichlet} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {419--422},
     year = {1990},
     volume = {33},
     number = {4},
     doi = {10.4153/CMB-1990-068-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-068-7/}
}
TY  - JOUR
AU  - Brown, Leon
TI  - Invertible Elements in the Dirichlet Space
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 419
EP  - 422
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-068-7/
DO  - 10.4153/CMB-1990-068-7
ID  - 10_4153_CMB_1990_068_7
ER  - 
%0 Journal Article
%A Brown, Leon
%T Invertible Elements in the Dirichlet Space
%J Canadian mathematical bulletin
%D 1990
%P 419-422
%V 33
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-068-7/
%R 10.4153/CMB-1990-068-7
%F 10_4153_CMB_1990_068_7

[1] 1. Berman, R., Brown, L., and Cohn, W., Cyclic vectors of bounded characteristic in Bergman spaces, Michigan Math. J. 31 (1984) 295–306. Google Scholar

[2] 2. Bourdon, P. S., Cyclic Nevanlinna class functions in Bergman spaces, Proc. Amer. Math. Soc. 93 (1985) 503–506. Google Scholar

[3] 3. Brown, L., Shields, A. L., Cyclic vectors in the Dirichlet space, Trans. Amer. Math. Soc. 285 (1984) 269–304. Google Scholar

[4] 4. Carleson, L., A Representation formula for the Dirichlet integral, Math. Z. 73 (1960) 190–196. Google Scholar

[5] 5. Richter, S., and Shields, A. L., Bounded analytic functions in the Dirichlet space, Math. Z. 198 (1988) 151–159. Google Scholar

[6] 6. Shamoyan, F. A., Weak invertibility in some spaces of analytic functions, Akad. Nauk Armyan, SSR Dokl.74 (1982) 157–161. Google Scholar

[7] 7. Shapiro, H. S., Weakly invertible elements in certain function spaces and generators in L\, Michigan Math. J. 11 (1964) 161–165. Google Scholar

[8] 8. Shields, A. L., Weighted shift operations and analytic function theory, Topics in operator theory (Pearcy, CM. Ed.) Math. Surveys 13, Amer. Math. Soc, Providence, R.I. (1974) 49-128 (second printing with addendum, 1979). Google Scholar

Cité par Sources :