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 -