TY - JOUR

T1 - On Hypo-Jordan operators

AU - Ko, Eungil

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035562233&partnerID=8YFLogxK

U2 - 10.1017/s001708950103004x

DO - 10.1017/s001708950103004x

M3 - Article

AN - SCOPUS:0035562233

SN - 0017-0895

VL - 43

SP - 411

EP - 418

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

IS - 3

ER -