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 -