TY - JOUR

T1 - Square roots of complex symmetric operators

AU - Jo, Munsun

AU - Ko, Eungil

AU - Lee, Ji Eun

N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - In this paper we study square roots of complex symmetric operators. In particular, we prove that if (Formula presented.) is a square root of a complex symmetric operator, then (Formula presented.) has the single-valued extension property if and only if so does T. Moreover, in this case, T has the Bishop's property (Formula presented.) if and only if T is decomposable. Finally, we show that if T has a nontrivial hyperinvariant subspace, then (Formula presented.) has a nontrivial invariant subspace.

AB - In this paper we study square roots of complex symmetric operators. In particular, we prove that if (Formula presented.) is a square root of a complex symmetric operator, then (Formula presented.) has the single-valued extension property if and only if so does T. Moreover, in this case, T has the Bishop's property (Formula presented.) if and only if T is decomposable. Finally, we show that if T has a nontrivial hyperinvariant subspace, then (Formula presented.) has a nontrivial invariant subspace.

KW - Square roots of complex symmetric operators

KW - nontrivial invariant subspace

KW - the Bishop's property

KW - the Dunford's property (C)

KW - the dunford's boundedness condition (B)

KW - the single-valued extension property

UR - http://www.scopus.com/inward/record.url?scp=85142674375&partnerID=8YFLogxK

U2 - 10.1080/03081087.2022.2146041

DO - 10.1080/03081087.2022.2146041

M3 - Article

AN - SCOPUS:85142674375

SN - 0308-1087

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

ER -