TY - JOUR
T1 - Hyperinvariant subspaces for some 2 × 2 operator matrices, II
AU - Jung, Il Bong
AU - Ko, Eungil
AU - Pearcy, Carl
N1 - Funding Information:
Acknowledgements. The first author was supported by the National Re-
Funding Information:
The first author was supported by the National Re-search Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (2018R1A2B6003660). The second author was supported by the Basic Science Re-search Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937).
Publisher Copyright:
© Kyungpook Mathematical Journal.
PY - 2019
Y1 - 2019
N2 - In a previous paper, the authors of this paper studied 2×2 matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1; 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the 2×2 matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such 2 × 2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.
AB - In a previous paper, the authors of this paper studied 2×2 matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1; 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the 2×2 matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such 2 × 2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.
KW - Compact operator
KW - Hyperinvariant subspace
KW - Invariant subspace
UR - http://www.scopus.com/inward/record.url?scp=85072561836&partnerID=8YFLogxK
U2 - 10.5666/KMJ.2019.59.2.225
DO - 10.5666/KMJ.2019.59.2.225
M3 - Article
AN - SCOPUS:85072561836
VL - 59
SP - 225
EP - 231
JO - Kyungpook Mathematical Journal
JF - Kyungpook Mathematical Journal
SN - 1225-6951
IS - 2
ER -