Geodesic
A distinction of k-hyponormal and weakly k-hyponormal weighted shifts
Filomat, Tome 35 (2021) no. 15, p. 5293

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Let α(x) : √ x 2 , √ 2 3 , √ 3 4 , √ 4 5 , ... be a sequence with a real variable x > 0 and let Wα(x) be the associated weighted shift with weight sequence α(x). In [17], Exner-Jung-Park provided an algorithm to distinguish weak k-hyponormality and k-hyponormality of weighted shift Wα(x), and obtained sn > 0 for some low numbers n = 4, ..., 10, such that Wα(sn) is weakly n-hyponormal but not n-hyponormal. In this paper, we obtain a formula of sn (for all positive integer n) such that Wα(sn) is weakly n-hyponormal but not n-hyponormal, which improves Exner-Jung-Park’s result above
DOI : 10.2298/FIL2115293L
Classification : 47B37, 47B20
Keywords: subnormal, polynomially hyponormal, k-hyponormal, weakly k-hyponormal, weighted shift 
Chunji Li; Mi Ryeong Lee; Yiping Xiao. A distinction of k-hyponormal and weakly k-hyponormal weighted shifts. Filomat, Tome 35 (2021) no. 15, p. 5293 . doi: 10.2298/FIL2115293L
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     title = {A distinction of k-hyponormal and weakly k-hyponormal weighted shifts},
     journal = {Filomat},
     pages = {5293 },
     year = {2021},
     volume = {35},
     number = {15},
     doi = {10.2298/FIL2115293L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2115293L/}
}
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