On Hypo-Jordan operators

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In this paper, we show that if T = S + N, where S is similar to a hyponormal operator, S and N commute and N is a nilpotent operator of order m (i.e., Nm = 0), then T is a subscalar operator of order 2m. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum σ(T) has the property that there exists some non-empty open set U such that σ(T) ∩ U is dominating for U.

Original languageEnglish
Pages (from-to)411-418
Number of pages8
JournalGlasgow Mathematical Journal
Issue number3
StatePublished - 2001


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