Year: 2025
Type: article
Abstract: In this paper, we study the minimality of the commutant of an analytic Toeplitz operator $$M_\varphi $$ M φ , when $$M_\varphi $$ M φ is defined on the Hardy space $$H^2(\mathbb {D})$$ H 2 ( D ) and $$\varphi \in H^\infty (\mathbb {D})$$ φ ∈ H ∞ ( D ) denotes a bounded analytic function in $$\mathbb {D}$$ D . Specifically, we show that the commutant of $$M_\varphi $$ M φ is minimal if and only if the polynomials on $$\varphi $$ φ are weak star dense in $$H^\infty (\mathbb {D})$$ H ∞ ( D ) , that is, $$\varphi $$ φ is a weak star generator of $$H^\infty (\mathbb {D})$$ H ∞ ( D ) . We use our result to characterize when the double commutant of an analytic Toeplitz operator $$M_\varphi $$ M φ is minimal for a large class of symbols $$\varphi $$ φ . Specifically, when $$\varphi $$ φ is an entire function, or more generally, when $$\varphi $$ φ belongs to the Thomson–Cowen class.
Institution: Universidad de Cádiz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Awards: G1175115578, G121809054, G143639328, G1826204064, G1855990336, G2262748287, G2309174360, G2357756629, G2390397592, G2585926585, G2660406951, G279363373, G2863668859, G300979063, G34346518, G3480869486, G425668148, G430777504, G4318065344, G4920779865, G4998806521, G5080475149, G514340343, G5421974903, G586857820, G7084143925, G7391727506, G846842501, G8920660035, G897484643, G99296377
OpenAlex ID: W4410033448