TY - JOUR
T1 - On operators with similar positive parts
AU - Ko, Eungil
N1 - Funding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (2016R1D1A1B03931937).
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.
AB - Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.
KW - Polar decomposition
KW - Similarity of positive parts
KW - Spectral property
UR - http://www.scopus.com/inward/record.url?scp=85044315487&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2018.03.032
DO - 10.1016/j.jmaa.2018.03.032
M3 - Article
AN - SCOPUS:85044315487
SN - 0022-247X
VL - 463
SP - 276
EP - 293
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -