Geodesic
Square roots of weighted shifts of multiplicity two
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 791-807

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DOI

Given a weighted shift T of multiplicity two, we study the set $\sqrt {T}$ of all square roots of T. We determine necessary and sufficient conditions on the weight sequence so that this set is non-empty. We show that when such conditions are satisfied, $\sqrt {T}$ contains a certain special class of operators. We also obtain a complete description of all operators in $\sqrt {T}$.
DOI : 10.4153/S000843952200073X
Mots-clés : Square roots, multipliers, weighted shift operators, weighted Hardy spaces 
Kottegoda, Chanaka; Le, Trieu; Rodriguez, Tomas Miguel. Square roots of weighted shifts of multiplicity two. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 791-807. doi: 10.4153/S000843952200073X
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     title = {Square roots of weighted shifts of multiplicity two},
     journal = {Canadian mathematical bulletin},
     pages = {791--807},
     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S000843952200073X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952200073X/}
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