On Some Properties of Cowen-Douglas Class of Operators
We will consider multiplication operators on a Hilbert space of analytic functions on a domain Ω⊂C. For a bounded analytic function φ on Ω, we will give necessary and sufficient conditions under which the complement of the essential spectrum of Mφ in φΩ becomes nonempty and this gives conditions for...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6078594 |
| Summary: | We will consider multiplication operators on a Hilbert space of analytic functions on a domain Ω⊂C. For a bounded analytic function φ on Ω, we will give necessary and sufficient conditions under which the complement of the essential spectrum of Mφ in φΩ becomes nonempty and this gives conditions for the adjoint of the multiplication operator Mφ belongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator. |
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| ISSN: | 2314-8896 2314-8888 |