• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.535-543
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• 2009

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition (B).

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.183-195
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• 2011

In this paper we show that Helton class preserves the nilpotent and finite ascent properties. Also, we show some relations on non-transitivity and decomposability between operators and their Helton classes. Finally, we give some applications in the Helton class of weighted shifts.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.509-517
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• 2006

In this Paper We Study some Operators With the single valued extension property. In particular, we investigate the Helton class of an operator and an $n{\times}n$ triangular operator matrix T.