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Subnormality of Bergman-like weighted shifts. (English) Zbl 1072.47027
For $$l\geq1$$, a Bergman-like weighted shift $$B_+^{(l)}$$ is the weighted shift with weight sequence $$\{\alpha_n^{(l)}\}_{n=0}^\infty$$, where $$\alpha_n^{(l)} = \sqrt{l-\frac{1}{n+2}}$$. For $$a,b,c,d\geq0$$ with $$ad-bc>0$$, denote by $$S(a,b,c,d)$$ the weighted shift with weight sequence $$\{\alpha_n\}_{n=0}^\infty$$, where $$\alpha_n=\sqrt{\frac{an+b}{cn+d}}$$. It is clear that $$B_+^{(l)}=S(l,2l-1,1,2)$$ for $$l\geq1$$. In the paper under review, the authors, using Schur product techniques, show that the weighted shifts $$S(a,b,c,d)$$ are subnormal and, for $$p\geq1$$, all $$p$$-subshifts of $$S(a,b,c,d)$$ are subnormal.

##### MSC:
 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B20 Subnormal operators, hyponormal operators, etc.
Mathematica
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