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Invertible Elements in the Dirichlet Space

Published online by Cambridge University Press:  20 November 2018

Leon Brown
Leon Brown*
Affiliation:
Mathematics Department Wayne State University Detroit, Michigan 48202
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Abstract

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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.

Keywords

30H0546E2047B37
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 419 - 422
Copyright
Copyright © Canadian Mathematical Society 1990

References

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. Bourdon, P. S., Cyclic Nevanlinna class functions in Bergman spaces, Proc. Amer. Math. Soc. 93 (1985) 503–506.Google Scholar
3. Brown, L., Shields, A. L., Cyclic vectors in the Dirichlet space, Trans. Amer. Math. Soc. 285 (1984) 269–304.Google Scholar
4. Carleson, L., A Representation formula for the Dirichlet integral, Math. Z. 73 (1960) 190–196.Google Scholar
5. Richter, S., and Shields, A. L., Bounded analytic functions in the Dirichlet space, Math. Z. 198 (1988) 151–159.Google Scholar
6. Shamoyan, F. A., Weak invertibility in some spaces of analytic functions, Akad. Nauk Armyan, SSR Dokl.74 (1982) 157–161.Google Scholar
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. 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