TY - JOUR
T1 - Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order
AU - Bonet, José
AU - Lindström, Mikael
AU - Wolf, Elke
N1 - Funding Information:
The research of José Bonet was partially supported by FEDER and MEC Project MTM 2007-62643 and Generalitat Valenciana project Prometeo/2008/101. Part of the present work was done during a stay of J. Bonet at the University of Paderborn in August 2008. The support of the Alexander von Humboldt Foundation is greatly appreciated.
PY - 2009/10
Y1 - 2009/10
N2 - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.
AB - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.
KW - Topological structure
KW - Weighted Bergman space of infinite order
KW - Weighted composition operator
UR - http://www.scopus.com/inward/record.url?scp=71549127718&partnerID=8YFLogxK
U2 - 10.1007/s00020-009-1706-x
DO - 10.1007/s00020-009-1706-x
M3 - Article
AN - SCOPUS:71549127718
SN - 0378-620X
VL - 65
SP - 195
EP - 210
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 2
ER -