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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.
Software:
Mathematica
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References:
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