Type of Document	Dissertation
Author	Zhong, Changyong
Author's Email Address	changyong.zhong@vanderbilt.edu
URN	etd-03232006-005345
Title	Multiplication Operators and M-Berezin Transforms
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Dechao Zheng Committee Chair Dietmar Bisch Committee Member Edward B. Saff Committee Member Guoliang Yu Committee Member Sokrates T. Pantelides Committee Member
Keywords	m-Berezin Transforms Reducing Subspaces Toeplitz Operators Hardy Space Bergman Space
Date of Defense	2006-03-20
Availability	unrestricted
Abstract Lattices of reducing subspaces of multiplication operators acting on the Bergman space induced by finite Blaschke products are studied. A complete description of the lattices of reducing subspaces of multiplication operators induced by Blaschke products of order three or order four is given. It is proved that, for the multiplication operator acting on the Bergman space induced by Blaschke product of order three or order four, the number of minimal reducing subspaces equals the number of connected components of the Riemann surface associated to the composition of the inverse of the Blaschke product and the Blaschke product itself. A characterization about the compactness of certain operators in the Toeplitz algebra acting on Bergman spaces of several complex variables is obtained via m-Berezin transforms.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    thesis.pdf 618.89 Kb 00:02:51 00:01:28 00:01:17 00:00:38 00:00:03