• 대한수학회보
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• 제53권5호
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• pp.1471-1481
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• 2016

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

• East Asian mathematical journal
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• 제31권5호
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.217-223
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• 2012

In this note we examine the effects on subnormality of adding a new weight or changing some weights for a given subnormal weighted shift. We consider a subnormal weighted shift with a positive point mass at the origin by means of continuous functions. Finally, we introduce some methods for evaluating point mass at the origin about moment measures associated with weighted shifts.

• 대한수학회보
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• 제51권4호
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• pp.1031-1040
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• 2014

In this paper, we show that any cubically hyponormal weighted shift with first two equal weights is flat. And we give an example of a weighted shift which is not cubically hyponormal but almost-cubically hyponormal.