Abstract
Abstract In this paper, we prove that the topological spaces of nonzero weighted composition operators acting on some Hilbert spaces of analytic functions on the unit open ball are simply connected.
Highlights
Let H( N ) be the space of analytic functions on the open unit ballN ≔ z = (z1,...,zN) ∈ N : ∥z∥2 = ∑ |zi |2 < i=1and H∞( N ) the space of bounded analytic functions on N with the supremum norm ∥⋅∥∞
Our main results are proved in Section 3; that is, we prove the topological spaces of nonzero weighted composition operators acting between certain Hilbert spaces of analytic functions on N are connected
We first study the topological spaces of weighted composition operators acting between general Hilbert spaces of analytic functions on N
Summary
Much effort has been expended on characterizing those analytic maps which induce bounded or compact composition operators between classical spaces of analytic functions. In 2005, Moorhouse [11] answered the question of compact difference of composition operators acting on Aλ2( ), λ > −1, and gave a partial answer to the component structure of (Aλ2( )). Our main results are proved in Section 3; that is, we prove the topological spaces of nonzero weighted composition operators acting between certain Hilbert spaces of analytic functions on N are connected.
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