| |
|
Hocine Guediri, Mubariz T. Garayev, and Houcine Sadraoui
The Bergman space as a Banach algebra view print
|
|
| Published: |
May 27, 2015
|
| Keywords: |
Duhamel product, Bergman space, extended eigenvalues, extended eigenoperators, cyclic vectors, intertwining relations, Banach ∗-algebra. |
| Subject: |
Primary 47B47; Secondary 47B38. |
|
|
Abstract
In this paper we use the Duhamel product to provide a Banach algebra structure to each of a scale of Bergman spaces over the unit disk, and then carry out many interesting consequences. In particular we characterize cyclic vectors of the Volterra integration operator, and determine its extended eigenvalues and corresponding extended eigenoperators. We also identify its commutants and point out some intertwining relations between the Volterra integration operator and composition operators.
|
|
| Acknowledgements
The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project no. RGP-VPP-323.
|
|
| Author information
Hocine Guediri:
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
hguediri@ksu.edu.sa
Mubariz T. Garayev:
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
mgarayev@ksu.edu.sa
Houcine Sadraoui:
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
sadrawi@ksu.edu.sa
|
|
