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Journal of Function Spaces
Volume 2018 (2018), Article ID 6078594, 6 pages
Research Article

On Some Properties of Cowen-Douglas Class of Operators

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Correspondence should be addressed to Bahmann Yousefi

Received 9 September 2017; Accepted 29 November 2017; Published 1 February 2018

Academic Editor: Kehe Zhu

Copyright © 2018 Parastoo Heiatian Naeini and Bahmann Yousefi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will consider multiplication operators on a Hilbert space of analytic functions on a domain . For a bounded analytic function on , we will give necessary and sufficient conditions under which the complement of the essential spectrum of in becomes nonempty and this gives conditions for the adjoint of the multiplication operator 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.