Path connected components in weighted composition operators on ℎ^{∞} and 𝐻^{∞} with the operator norm

Izuchi, Kei; Izuchi, Yuko; Ohno, Shûichi

doi:10.1090/S0002-9947-2012-05730-8

Path connected components in weighted composition operators on $h^\infty$ and $H^\infty$ with the operator norm
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Trans. Amer. Math. Soc. 365 (2013), 3593-3612 Request permission

Abstract:

We consider the component problem on the sets of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk with the operator norms, respectively. Especially, we shall determine path connected components in the sets of noncompact weighted composition operators.

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