TY - JOUR

T1 - Square roots of hyponormal operators

AU - Kim, Mee Kyoung

AU - Eungil, K. O.

PY - 1999

Y1 - 1999

N2 - An operator T ε ℒ(H) is called a square root of a hyponormal operator if T2 is hyponormal. In this paper, we prove the following results: Let S and T be square roots of hyponormal operators. (1) If σ(T) ∩ [-σ(T)] = φ or {0}, then T is isoloid (i.e., every isolated point of σ(T) is an eigenvalue of T). (2) If S and T commute, then ST is Weyl if and only if S and T are both Weyl. (3) If σ(T) ∩ [-σ(T)] = φ or {0}, then Weyl's theorem holds for T. (4) If σ(T) ∩ [-σ(T)] = φ, then T is subscalar. As a corollary, we get that T has a nontrivial invariant subspace if σ(T) has non-empty interior. (See [3].)

AB - An operator T ε ℒ(H) is called a square root of a hyponormal operator if T2 is hyponormal. In this paper, we prove the following results: Let S and T be square roots of hyponormal operators. (1) If σ(T) ∩ [-σ(T)] = φ or {0}, then T is isoloid (i.e., every isolated point of σ(T) is an eigenvalue of T). (2) If S and T commute, then ST is Weyl if and only if S and T are both Weyl. (3) If σ(T) ∩ [-σ(T)] = φ or {0}, then Weyl's theorem holds for T. (4) If σ(T) ∩ [-σ(T)] = φ, then T is subscalar. As a corollary, we get that T has a nontrivial invariant subspace if σ(T) has non-empty interior. (See [3].)

UR - http://www.scopus.com/inward/record.url?scp=0038353867&partnerID=8YFLogxK

U2 - 10.1017/S0017089599000178

DO - 10.1017/S0017089599000178

M3 - Article

AN - SCOPUS:0038353867

VL - 41

SP - 463

EP - 470

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 3

ER -