Abstract
We investigate the topological connectedness of the set of composition operators on the weighted Bergman space A α 2 under the uniform operator topology. One of our main results is to first find a necessary and sufficient condition for two composition operators on A α 2 to be linearly connected in the case of one variable. As a corollary, we show that two composition operators on A α 2 with compact difference must lie in the same path component.
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