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In this paper, we introduce a new notion of completely semi-weakly hyponormal operator which is a special case of polynomially hyponormal operator. For an one-step backward extension of the Bergman… Click to show full abstract
In this paper, we introduce a new notion of completely semi-weakly hyponormal operator which is a special case of polynomially hyponormal operator. For an one-step backward extension of the Bergman weighted shift, we show that completely semi-weakly hyponormal weighted shifts need not be subnormal. In addition, we provide an example which can serve to distinguish the semi-weak $m$-hyponormality from the semi-weak $m$-hyponormality with positive determinant coefficients for such a shift. Finally we discuss flatness on semi-weakly $m$-hyponormal weighted shifts.
Journal Title: Filomat
Year Published: 2017
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