Berezin symbols and operator theory
| dc.contributor.author | Potter, Michael James A. | en_US |
| dc.date.accessioned | 2007-06-01T19:23:40Z | |
| dc.date.available | 2007-06-01T19:23:40Z | |
| dc.date.issued | 2000-05-01T00:00:00Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | Let 'H' be a standard analytic functional Hilbert space over a bounded domain [Omega] ? C. We examine the Berezin symbols 'A~' of bounded operators A?BH and characterize the compact operators KH by Berezin symbol behavior. We show that A?KH iff the Berezin symbol of every unitary conjugate of 'A' is in 'C'0([Omega]) (Nordgren and Rosenthal, 1994). Special attention is also given to examples and the theory of Berezin symbols on the Bergman and Hardy space. We show a characterization (Axler and Zheng, 1998) of compact Toeplitz operators on the Bergman space that generalizes to Hankel operators. The condition 'A' is compact iff A*A&d15;z [right arrow]0 as @'z'@ [right arrow] 1- holds for all Toeplitz, Hankel, and composition operators on both the Bergman and Hardy spaces. | en_US |
| dc.format.extent | 2666523 bytes | |
| dc.format.extent | 184 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | text/plain | |
| dc.identifier.uri | http://hdl.handle.net/1993/2395 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.title | Berezin symbols and operator theory | en_US |
| dc.type | master thesis | en_US |