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Amiri, S.; Golbaharan, A.; Mahyar, H.

Weighted composition operators on analytic Lipschitz spaces. (English) Zbl 1503.47031

Result. Math. 73, No. 1, Paper No. 46, 15 p. (2018).
Summary: We study boundedness and compactness of weighted composition operators on spaces of analytic Lipschitz functions \(\mathrm{Lip}_A(X, \alpha )\) where \(X\) is a compact plane set and \(0<\alpha \leq 1\). We give necessary conditions for these operators to be compact, we also provide some sufficient conditions for the compactness of such operators. In the case of \(0<\alpha <1\), to obtain the necessary condition we consider the relationship between these spaces and Bloch type spaces \(\mathcal {B}^\alpha \). We then conclude some results about boundedness and compactness of weighted composition operators on \(\mathcal {B}^\alpha \). Finally, we determine the spectra of compact (Riesz) weighted composition operators acting on analytic Lipschitz spaces or on Bloch type spaces. Also as a consequence, we characterize power compact composition operators on these spaces.

Cited in 2 Documents

MSC:

47B33 Linear composition operators
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30H30 Bloch spaces
30H50 Algebras of analytic functions of one complex variable

Keywords:

weighted composition operators; analytic Lipschitz algebras; Bloch-type spaces; spectra; compact; Riesz; quasicompact operators
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References:

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