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...
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Hindawi Limited
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6078594 |
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doaj-6fbc96f6bbee4dbf89726f0e2905a5ab2020-11-25T00:59:07ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/60785946078594On Some Properties of Cowen-Douglas Class of OperatorsParastoo Heiatian Naeini0Bahmann Yousefi1Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, IranDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, IranWe 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.http://dx.doi.org/10.1155/2018/6078594 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Parastoo Heiatian Naeini Bahmann Yousefi |
| spellingShingle |
Parastoo Heiatian Naeini Bahmann Yousefi On Some Properties of Cowen-Douglas Class of Operators Journal of Function Spaces |
| author_facet |
Parastoo Heiatian Naeini Bahmann Yousefi |
| author_sort |
Parastoo Heiatian Naeini |
| title |
On Some Properties of Cowen-Douglas Class of Operators |
| title_short |
On Some Properties of Cowen-Douglas Class of Operators |
| title_full |
On Some Properties of Cowen-Douglas Class of Operators |
| title_fullStr |
On Some Properties of Cowen-Douglas Class of Operators |
| title_full_unstemmed |
On Some Properties of Cowen-Douglas Class of Operators |
| title_sort |
on some properties of cowen-douglas class of operators |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2018-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2018/6078594 |
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AT parastooheiatiannaeini onsomepropertiesofcowendouglasclassofoperators AT bahmannyousefi onsomepropertiesofcowendouglasclassofoperators |
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1725218798255996928 |