Geodesic
Volterra-type operators on the minimal Möbius-invariant space
Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 509-524

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DOI

In this note, we mainly study operator-theoretic properties on the Besov space $B_{1}$ on the unit disk. This space is the minimal Möbius-invariant space. First, we consider the boundedness of Volterra-type operators. Second, we prove that Volterra-type operators belong to the Deddens algebra of a composition operator. Third, we obtain estimates for the essential norm of Volterra-type operators. Finally, we give a complete characterization of the spectrum of Volterra-type operators.
DOI : 10.4153/S0008439522000376
Mots-clés : Volterra-type operators, minimal Möbius-invariant space, Deddens algebra 
Xie, Huayou; Liu, Junming; Ponnusamy, Saminathan. Volterra-type operators on the minimal Möbius-invariant space. Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 509-524. doi: 10.4153/S0008439522000376
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     title = {Volterra-type operators on the minimal {M\"obius-invariant} space},
     journal = {Canadian mathematical bulletin},
     pages = {509--524},
     year = {2023},
     volume = {66},
     number = {2},
     doi = {10.4153/S0008439522000376},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000376/}
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